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1.
VCO sweep-rate limit for a phase-lock loop 总被引：1，自引：0，他引：1
John Stensby 《Journal of The Franklin Institute》2009,346(3):223-236
Phase-lock loops (PLLs) serve important roles in phase-lock receivers, coherent transponders, and similar applications. For many of these uses, the bandwidth of the loop must be kept small to limit the detrimental influence of noise, and this requirement makes the natural PLL pull-in phenomenon too slow and/or unreliable. For each such case, the phase-lock acquisition process can be aided by the application of an external sweep voltage to the loop voltage controlled oscillators (VCOs). The goal is to have the applied sweep voltage rapidly decrease the closed-loop frequency error to a point where phase lock occurs quickly. For a second-order loop containing a perfect integrator loop filter, there is a maximum VCO sweep-rate magnitude, denoted here as Rm rad/s2, for which phase lock is guaranteed. If the applied VCO sweep rate is less than Rm, the loop cannot sweep past a stable phase-lock point, and it will phase lock. On the other hand, for an applied sweep-rate magnitude that is greater than Rm, the PLL may sweep past a lock point and fail to phase lock. In the existing PLL literature, only a trial-and-error approach has been described for estimating Rm, given values of loop damping factor ζ and natural frequency ωn. Furthermore, no plots exist of computed versus ζ and versus ζ (BL denotes loop-noise bandwidth). These deficiencies are dealt with in this paper. A new iterative numerical technique is given that converges to the maximum sweep-rate magnitude Rm. It is used to generate data for plots of and versus ζ, the likes of which have never appeared before in the PLL literature. 相似文献
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Leitao Gao Guangshe Zhao Guoqi Li Lei Deng Fei Zeng 《Journal of The Franklin Institute》2018,355(16):8141-8157
Determining an input matrix, i.e., locating predefined number of nodes (named “key nodes”) connected to external control sources that provide control signals, so as to minimize the cost of controlling a preselected subset of nodes (named “target nodes”) in directed networks is an outstanding issue. This problem arises especially in large natural and technological networks. To address this issue, we focus on directed networks with linear dynamics and propose an iterative method, termed as “L0-norm constraint based projected gradient method” (LPGM) in which the input matrix B is involved as a matrix variable. By introducing a chain rule for matrix differentiation, the gradient of the cost function with respect to B can be derived. This allows us to search B by applying probabilistic projection operator between two spaces, i.e., a real valued matrix space RN?×?M and a L0 norm matrix space by restricting the L0 norm of B as a fixed value of M. Then, the nodes that correspond to the M nonzero elements of the obtained input matrix (denoted as ) are selected as M key nodes, and each external control source is connected to a single key node. Simulation examples in real-life networks are presented to verify the potential of the proposed method. An interesting phenomenon we uncovered is that generally the control cost of scale free (SF) networks is higher than Erdos-Renyi (ER) networks using the same number of external control sources to control the same size of target nodes of networks with the same network size and mean degree. This work will deepen the understanding of optimal target control problems and provide new insights to locate key nodes for achieving minimum-cost control of target nodes in directed networks. 相似文献
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Xingping Sheng 《Journal of The Franklin Institute》2018,355(10):4282-4297
The present work proposes a relaxed gradient based iterative (RGI) algorithm to find the solutions of coupled Sylvester matrix equations . It is proved that the proposed iterative method can obtain the solutions of the coupled Sylvester matrix equations for any initial matrices X0 and Y0. Next the RGI algorithm is extended to the generalized coupled Sylvester matrix equations of the form . Then, we compare their convergence rate and find RGI is faster than GI, which has maximum convergence rate, under an appropriative positive number ω and the same convergence factor µ1 and µ2. Finally, a numerical example is included to demonstrate that the introduced iterative algorithm is more efficient than the gradient based iterative (GI) algorithm of (Ding and Chen 2006) in speed, elapsed time and iterative steps. 相似文献
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Determining the thermal conductivity of iron alloys at high pressures and temperatures are essential for understanding the thermal history and dynamics of the Earth''s metallic cores. The authors summarize relevant high-pressure experiments using a diamond-anvil cell and discuss implications of high core conductivity for its thermal and compositional evolution.The thermal conductivity of iron alloys is a key to understanding the mechanism of convection in the Earth''s liquid core and its thermal history. The Earth''s magnetic field is formed by a dynamo action that requires convection in the liquid core. Present-day outer core convection can be driven by the buoyancy of light-element-enriched liquid that is released upon inner core solidification in addition to thermal buoyancy associated with secular cooling. In contrast, before the birth of the inner core, the core heat loss must be more than the heat conducted down the isentropic gradient in order to drive convection by thermal buoyancy alone, which can be a tight constraint upon the core thermal evolution.Recent mineral physics studies throw the traditional value of the Earth''s core thermal conductivity into doubt (Fig. (Fig.1).1). Conventionally the thermal conductivity of the outer core had been considered to be ∼30 W m−1 K−1, an estimate based on shock experiments and simple physical models including the Wiedemann-Franz law: κel = LTρ−1, where κel, L, T and ρ are electronic thermal conductivity, Lorenz number, temperature and electrical resistivity, respectively [1]. Such relatively low core conductivity indicates that liquid core convection could have been driven thermally even with relatively slow cooling rate. However, in 2012–2013, our conventional view was challenged by both computational and experimental studies showing much higher core conductivity [2–4].Open in a separate windowFigure 1.(a) Electrical resistivity and (b) thermal conductivity values at the top of the Earth''s core in the literature [1,2,4–7,9,16]. Filled symbols were calculated on the basis of the Wiedemann-Franz law with ideal Lorenz number (L0 = 2.44 × 10−8 W Ω K−2). Gray bands indicate (a) the range of saturation resistivity [9] and (b) thermal conductivity computed from the saturation resistivity and the Wiedemann-Franz law.Since then, experimental determinations of the thermal conductivity of iron and alloys have been controversial (Fig. (Fig.1).1). Ohta et al. [5] measured the electrical resistivity of iron under core conditions in a laser-heated diamond-anvil cell (DAC). The results demonstrate relatively high thermal conductivity of ∼90 W m−1 K−1 for liquid Fe-Ni-Si alloy based on their measured resistivity for pure iron, Matthissen''s rule and Wiedemann-Franz law, which is compatible with ab initio simulations [2,4]. On the other hand, flash laser-heating and fast thermal radiation detection experiments demonstrated the low core conductivity of 20–35 W m−1 K−1 based on finite element method simulations [6,7], in accordance with the traditional estimate [1]. Since transport properties that describe non-equilibrium phenomena are difficult to measure, the fact that determinations of the iron conductivity under core conditions have become viable these days is a remarkable success in mineral physics. Nevertheless, the discrepancy in core conductivity makes a big difference in the expected age of the inner core, mechanism of liquid core convection and thermal history [3].Despite a number of subsequent studies based on a variety of different techniques, we still see a dichotomy of proposed core conductivity values (Fig. (Fig.1).1). The ‘saturation’ resistivity, which is derived from the fact that the mean free path of electron–phonon interaction cannot be longer than the interatomic distance, gives the lower bound for conductivity. Such saturation resistivity lies between two clusters of reported high and low resistivity values. While the resistivity saturation is important in highly resistive transition metals and their alloys [3,8] (Fig. (Fig.2),2), the conventional estimate [1] did not include the effect of saturation in their models, which resulted in much higher resistivity than the saturation value and hence low core conductivity. The core electrical resistivity measured by recent DAC experiments [3,5,9] shows resistivity saturation (Fig. (Fig.2),2), demonstrating the high core conductivity as far as the Wiedemann-Franz law holds with ideal Lorenz number (Fig. (Fig.1).1). Additionally, since temperature has a large effect on resistivity, temperature gradient in a laser-heated sample is an issue. An internally-resistance-heated DAC provides homogenous and stable sample heating and is thus a promising technique for conductivity measurements at high pressure and temperature (P–T) [9]. The validity of the Wiedemann-Franz law under extreme conditions has also been an issue. Simultaneous measurements of the electrical resistivity and the thermal conductivity of iron alloy under core high P–T conditions will provide decisive evidence for it.Open in a separate windowFigure 2.Temperature response of the electrical resistivity of (a) fcc iron estimated at 1 bar [8] (blue curve) and (b) hcp iron at 115 GPa [5]. Red curve and black line with gray uncertainty band indicate the predicted resistivity based on the Bloch-Grüneisen model with and without the resistivity saturation, respectively.As introduced above, the most recent high P–T measurements for Fe containing 2, 4, 6.5 wt.% Si using an internally-resistance-heated DAC have demonstrated that the thermal conductivity of Fe-12.7 wt.% (22.5 at.%) Si is ∼88 W m−1 K−1 at core-mantle boundary (CMB) conditions when the effects of resistivity saturation, melting and crystallographic anisotropy at measurements are taken into account [9] (Fig. (Fig.1).1). Thermal conductivity of Fe-10 at.% Ni-22.5 at.% Si alloy, a possible outer core composition, could be ∼79 W m−1 K−1 considering the impurity effect of Ni [10]. Si exhibits the largest ‘impurity resistivity’, indicating that the 79 W m−1 K−1 is the lower bound for the thermal conductivity of the Earth''s liquid core. The core thermal evolution models by Labrosse [11] demonstrated that if liquid core convection has been driven by thermal buoyancy with the core thermal conductivity of 79 W m−1 K−1 at the CMB and no radiogenic heating in the core, the CMB temperature is calculated to be ∼5500 K at 3.2 Ga and ∼4800 K at 2.0 Ga. Such high CMB temperature suggests that the whole mantle was fully molten until 2.0–3.2 Ga. It is not consistent with geological records, calling for a different mechanism of core convection.Chemical buoyancy may be an alternate means of driving convection in the core from the early history of the Earth. It has been proposed that the compositional buoyancy in the core could arise from the exsolution of MgO, SiO2 or both [12–14]. Recent core formation models based on the core-mantle distributions of siderophile elements suggest that core metals segregated from silicate at high temperatures, typically at 3000–4000 K and possibly higher [13,15], which enhances the incorporation of lithophile elements including Si and O, and possibly Mg into metals. It is suggested that the (Si, O)-rich liquid core may have become saturated with SiO2 upon secular cooling [14]. Indeed, the original core compositions proposed in recent core formation models include Si and O beyond the saturation limit at CMB conditions [15], i.e. 136 GPa and 4000 K, leading to SiO2 crystallization [13]. The rate of SiO2 crystallization required to sustain geodynamo is as low as 1 wt.% per 109 years, which corresponds to a cooling rate of 100–200 K Gyr−1 [14]. The most recent model of the core compositional evolution by Helffrich et al. [13] showed that MgO saturation follows SiO2 saturation only when >1.7 wt.% Mg in the core. If this is the case, in addition to solid SiO2, (Mg, Fe)-silicate melts exsolve from the core and transfer core-hosted elements such as Mo, W and Pt to the mantle. The core-derived silicate melts may have evolved toward FeO-rich compositions and now represent the ultra-low velocity zones above the CMB. 相似文献
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This work is devoted to the study of symmetric control systems. It establishes a relation between internal symmetry and external one for a linear invariant control system having n real simple poles. The symmetric stabilization problem is studied using a symmetric feedback gain such that the output control stabilizes the closed-loop system. A necessary and sufficient condition is given to solve this stabilization problem for a symmetric control system (A,B,C) and a generalized symmetric control system (E,A,B,C). 相似文献
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Akbar Zada Bakht Zada Jinde Cao Tongxing Li 《Journal of The Franklin Institute》2017,354(14):6247-6257
Let {Πτ(m, n): m?≥?n?≥?0} be the family of periodic discrete transition matrices generated by bounded valued square matrices Λτ(n), where is an arbitrary switching signal. We prove that the family {Πτ(m, n): m?≥?n?≥?0} of bounded linear operator is uniformly exponentially stable if and only if the sequence is bounded. 相似文献
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Jianwei Xia Hui Gao Mingxin Liu Guangming Zhuang Baoyong Zhang 《Journal of The Franklin Institute》2018,355(6):3031-3049
In this paper, the issues of finite-time extended dissipative analysis and non-fragile control are investigated for a class of uncertain discrete time switched linear systems. Based on average dwell-time approach, sufficient conditions for the finite-time boundedness and finite-time extended dissipative performance of the considered systems are proposed by solving some linear matrix inequalities, where using the concept of extended dissipative, we can solve the H∞, Passivity and (Q, S, R)-dissipativity performance in a unified framework. Furthermore, two form of non-fragile state feedback controllers are designed to guarantee that the closed-loop systems satisfy the finite-time extended dissipative performance. Finally, simulation example is given to show the efficiency of the proposed methods. 相似文献
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Olivier Ducloux Elisabeth Galopin Farzam Zoueshtiagh Alain Merlen Vincent Thomy 《Biomicrofluidics》2010,4(1)
A droplet-based micro-total-analysis system involving biosensor performance enhancement by integrated surface-acoustic-wave (SAW) microstreaming is shown. The bioreactor consists of an encapsulated droplet with a biosensor on its periphery, with in situ streaming induced by SAW. This paper highlights the characterization by particle image tracking of the speed distribution inside the droplet. The analyte-biosensor interaction is then evaluated by finite element simulation with different streaming conditions. Calculation of the biosensing enhancement shows an optimum in the biosensor response. These results confirm that the evaluation of the Damköhler and Peclet numbers is of primary importance when designing biosensors enhanced by streaming.It has been pointed out that biosensing performances can be limited by the diffusion of the analytes near the sensing surface.1 In the case of low Peclet number hydrodynamic flows, typical of microfluidic systems, molecule displacements are mainly governed by diffusive effects that affect time scales and sensitivity. To overcome this problem, the enhancement of biosensor performance by electrothermal stirring within microchannels was first reported by Meinhart et al.2 Other authors3, 4 numerically studied the analyte transport as a function of the position of a nanowire-based sensor inside a microchannel, stressing on the fact that the challenge for nanobiosensors is not the sensor itself but the fluidic system that delivers the sample. Addressing this problem, Squires et al.5 developed a simple model applicable to biosensors embedded in microchannels. However, the presented model is limited to the case of a steady flow. The use of surface-acoustic waves (SAWs) for stirring in biomicrofluidic and chemical systems is becoming a popular investigation field,6, 7, 8, 9 especially to overcome problems linked to steady flows by enhancing the liquid∕surface interaction.1, 10, 11 The main challenges that need to be addressed when using SAW-induced stirring are the complexity of the flow and its poor reproducibility. However, some technical solutions were proposed to yield a simplified microstreaming. Yeo et al. presented a centrifugation system based on SAW that produces the rotation of the liquid in a droplet in a reproducible way by playing on the configuration of the transducers and reflectors,12 and presented a comprehensive experimental study of the three-dimensional (3D) flow that causes particle concentration in SAW-stirred droplets,13 revealing the presence of an azimuthal secondary flow in addition to the main vortexlike circular flow present in acoustically stirred droplets. The efficiency of SAW stirring in microdroplets to favorably cope with mass transport issues was finally shown by Galopin et al.,14 but the effect of the stirring on the analyte∕biosensor interaction was not studied. It is expected to overcome mass transport limitations by bringing fresh analytes from the bulk solution to the sensing surface.The studied system, described in Fig. Fig.1,1, consists of a microliter droplet microchamber squeezed between a hydrophobic piezoelectric substrate and a hydrophobic glass cover. Rayleigh SAWs are generated using interdigitated transducers (interdigital spacing of 50 μm) laid on an X-cut LiNbO3 substrate.1, 15, 16 The hydrophobicity of the substrate and the cover are obtained by grafting octadecyltrichlorosilane (OTS) self-assembled monolayers (contact angle of 108° and hysteresis of 9°). To do so, the surface is first hydroxylized using oxygen plasma (150 W, 100 mT, and 30 sccm3 O2) during 1 min and then immersed for 3 h into a 1 mM OTS solution with n-hexane as a solvent.Open in a separate windowFigure 1(a) General view of the considered system. (b) Mean value of the measured speeds within the droplet as a function of the inlet power before amplification.When Rayleigh waves are radiated toward one-half of the microchamber, a vortex is created in the liquid around an axis orthogonal to the substrate due to the momentum transfer between the solid and the liquid. This wave is generated under the Rayleigh angle into the liquid.Speed cartographies of the flow induced in the droplet are realized using the particle image tracking technique for different SAW generation powers. To do so, instantaneous images of the flow are taken with a high-speed video camera at 200 frames∕s and an aperture time of 500 μs on a 0.25 μl droplet containing 1 μm diameter fluorescent particles. Figure Figure11 shows the mean speed measured in the droplet as a function of the inlet power. The great dependence of the induced mean speed with the SAW power enables a large range of flow speeds in the stirred droplet. Moreover, the flow was visualized with a low depth of field objective. It was found to be circular and two dimensional (2D) in a large thickness range of the droplet.The binding of analytes to immobilized ligands on a biosensor is a two step process, including the mass transport of the analyte to the surface, followed by a complexation step,(1)with km as the constant rate for mass transport from and to the sensor, and ka and kd as the constant rates of association and dissociation of the complex.At the biosensor surface, the reaction kinetics consumes analytes but their transport is limited by diffusive effects. In this case, the Damköhler number brings valuable information by comparing these two effects. Calling the characteristic time of reaction and diffusion, respectively, τC and τM, the mixing time in diffusion regime can be approximated by τM≈h2∕D with D as the diffusion coefficient and h a characteristic length of the microchannel. Calling RT the ligand concentration on the surface in mole∕m2, the Damköhler number (Da) can be written as(2)Depending on the type of reaction, the calculation of Da helps determine if a specific biointeraction will benefit from a mass SAW-based microstreaming. If the Damköhler number is low, the reaction is slow compared to mass transport and the reaction will not significantly benefit from microstirring. For example, the hybridization of 19 base single stranded DNA in a microfluidic system with a characteristic length of 500 μm is characterized by a Damköhler number of 0.07 and is therefore not significantly influenced by mass transport. On the contrary, the binding of biotin to immobilized streptavidin is characterized by a Da number of approximately 104. In this case, the stirring solution will significantly improve the reaction rate.COMSOL numerical simulations were carried out to study the efficiency of the SAW stirring in the case of a droplet-based microbioreactor with a diameter of 1 mm. Assuming a 2D flow, the simulated model takes into account the convective and diffusive effects in the analyte-carrying fluid and the binding kinetics on the biosensor surface. This approach was thoroughly developed by Meinhart et al.2On the biosensor surface, the following equations are solved:(3)(4)with c as the local concentration of analytes in the droplet and B as the surface concentration of bound analytes on the biosensor surface. Simulation results show that a depleted zone is formed near the biosensor in the case of an interaction without stirring. This zone is characterized by a low concentration of analytes and results from the trapping of analytes on the biosensor surface, thus creating a concentration gradient on the vicinity of the biosensor. When stirring is applied, the geometry of the depleted zone is modified, as it is pushed in the direction of the flow. The geometry of the depleted zone then depends on many parameters, among which the diffusion coefficient D, the speed distribution of the flow (not only near the biosensor but also in the whole microfluidic system), and the reaction kinetics on the biosensor. In our case, which is assimilated to a simple circular flow, the depleted zone reaches a permanent state consisting of an analyte-poor layer situated in the exterior perimeter of the stirred droplet. The diffusion of analytes is then limited again by diffusion from the inner part of the droplet toward its exterior perimeter (see Fig. Fig.22).Open in a separate windowFigure 2(a) Mean concentration of bound analytes vs time for different mean flow speeds. (b) The obtained concentration profiles with and without circular stirring, t=10 000 s.The initial analyte and receptor concentrations are, respectively, 0.1 nM in the solution and 3.3×10−3 nM m on the biosensor surface, the diffusion coefficient is D=10−11 m2 s−1, and the reaction constants are ka=106 M−1 s−1 and kd=10−3 s−1. Simulations show that the mean concentration of bound analytes highly increases with the flow speed, improving the efficiency of the biosensing device. To evaluate the benefits of in situ microstreaming with SAW, the same simulations were conducted for Da numbers ranging from 104 to 108 M−1∕s, by ranging the diffusion coefficient from 4×10−12 to 4×10−9 m2∕s, and the association coefficient ka from 104 to 108 M−1∕s. The enhancement factor of analyte capture, defined as the ratio of the binding rate with streaming B and the binding rate without streaming B0, is plotted in Fig. Fig.33 for different values of Da. Calculations are done in the case of a mean flow speed of 0.5 mm∕s.Open in a separate windowFigure 3(a) Enhancement factor (defined as the ratio between binding rate with streaming B and binding rate without streaming B0) for different Damkhöler numbers and (b) normalized enhancement factor for different Peclet numbers.One can notice the saturation of the enhancement factor curve for large value of Da to the value of 3.5 for high Da. This can be explained by the fact that for large ka∕Da ratios, the analytes, which normally require penetration in the depleted zone by diffusion, do not have time to interact with the biosensor when they pass in the vicinity of its surface. The efficiency of the streaming is then reduced for large values of Da. In the case of our specific flow configuration, the enhancement factor reaches 3.2 for the interaction of streptavidin on immobilized biotin (Da=103).The reported simulation results can be compared to an experimental value obtained using the droplet-based surface plasmon resonance sensor streamed in situ using SAW reported by Yeo et al.12 By monitoring the streptavidin∕biotin binding interaction on an activated gold slide, they showed that SAW stirring brings an improvement factor of more than 2. This difference can be accounted to the high complexity of the induced 3D flow, which was modeled in a simple manner in our calculations.Other factors must be taken into account when optimizing the improvement factor, such as the flow velocity and the characteristic length of the mixing. To do so, the Peclet number allows the comparison of the convective and diffusive effects.17 For δC a typical variation in concentration on the distance h, the Peclet number is given by(5)A significantly high Peclet number causes a decrease in biosensing efficiency as the analytes do not have enough time to interact with the biosensing surface by diffusion through the analyte-poor layer. On the contrary, the case of a low Peclet number corresponds to the diffusion-limited problem. Therefore, for each Damköhler number, there is a Peclet number optimizing this factor. To illustrate this fact, Fig. Fig.3b3b shows the calculation of the enhancement factor as a function of the Peclet number for a given Da.In this paper, we showed that surface loading of typical analytes on a droplet-based biosensor can be highly increased by SAW microstirring. The system permits the enhancement of the biosensing performances by the continuous renewal of the analyte-carrying fluid near the sensing surface. Thanks to mean flow speeds measured up to 1800 μm∕s, the SAW microstreaming can be beneficial to the biosensing of a large range of analyte∕ligand interactions. In addition to the biosensing performance improvement, such a method can be easily integrated in micro-micro-total-analysis systems, which makes it a convenient tool for liquid handling in future biochips. 相似文献
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Xiongping Dai Tingwen Huang Yu Huang Yi Luo Gang Wang Mingqing Xiao 《Journal of The Franklin Institute》2017,354(10):4126-4155
Given any finite family of real d-by-d nonsingular matrices by extending the well-known Li–Yorke chaos of a deterministic nonlinear dynamical system to a discrete-time linear inclusion or hybrid or switched system:
we study the chaotic dynamics of the state trajectory (xn(x0, σ))n ≥ 1 with initial state governed by a switching law . Two sufficient conditions are given so that for a “large” set of switching laws σ, there exhibits the scrambled dynamics as follows: for all This implies that there coexist positive, zero and negative Lyapunov exponents and that the trajectories (xn(x0, σ))n ≥ 1 are extremely sensitive to the initial states . We also show that a periodically stable linear inclusion system, which may be product unbounded, does not exhibit any such chaotic behavior. An explicit simple example shows the discontinuity of Lyapunov exponents with respect to the switching laws. 相似文献
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F.M. Reza 《Journal of The Franklin Institute》1982,314(3):191-202
The natural modes of an underdamped dynamical system are given by the characteristic numbers of the quadratic operator pencil where the operator A depends on the dissipative and reactive elements of the system, while B depends solely on the reactive elements. The operator P(s) for every applied stimulus vector signal x must satisfy: A measure of underdamped behaviour is suggested by predetermining an angular region |φ| containing all natural modes of the system, When a comparison between positive operators A and B is available, say B2=KA, then The paper is motivated by Duffin-Krein-Gohberg's earlier mathematical contributions. 相似文献
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This paper mainly concerns N-step off-line suboptimal predictive controller design for discrete nonhomogeneous Markov jump systems, in which the Markov chains are time-varying transition probabilities matrix modeled as a polytope. The design procedure is divided into N-step, more precisely, the first is to design the Nth step when the changes of Euclidean form of mode-dependent feedback law between the Nth and the (N+1)th asymptotically stable mode-dependent ellipsoids are less than the given accuracy. Then the N th asymptotically stable mode-dependent invariant ellipsoid is defined. In the previous (N−1) steps, an off-line mode-dependent predictive controller is designed to drive the state to this small area including the origin. Compared with on-line MPC algorithm, the computation time is dramatically reduced while the dynamic performance of controller is comparable. One numerical example is presented to illustrate the validity of the developed results. 相似文献
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This paper is concerned with non-fragile control problems for a class of continuous-time nonlinear systems with unknown nonlinearity and quantized inputs and outputs. The construction of both static output feedback (SOF) and observer-based output feedback (OBOF) control laws in the presence of additive interval-bounded controller coefficient variations can be divided into two parts, linear and nonlinear parts. The linear part plays a role in achieving the performance, while the nonlinear part is used to reduce the quantization effect. However, it should be pointed out that the effect of input and output quantization can be eliminated fully for SOF case by requiring knowledge of all signs of the states, but only the effect of input quantization can be eliminated for OBOF case. It is worth mentioning that three novel alternative methods with strict linear matrix inequality (LMI) conditions are proposed to design both SOF and OBOF controllers. In particular, these three new methods do not introduce any other auxiliary constraints as many existing results do where a matrix equality constraint between system matrix and Lyapunov matrix is often inserted. Finally, the effectiveness and advantages of the proposed control methods are demonstrated by a numerical example. 相似文献
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