共查询到20条相似文献，搜索用时 46 毫秒
1.
The bounded-input bounded-output stability, finite time stability and settling time of a single-loop feedback system consisting of a nonlinear time-varying gain followed by a linear time-invariant system are investigated via a nonlinear integral inequality. The gain has the form k0+k1(t)+k2(t)g(bd) where g(bd) is a monotonic increasing function. The system is bounded-input bounded-output stable provided the time-varying gains are L1(0, t8) functions and is finite time stable for bounded gains. The nonlinear integral inequality, which is used to obtain explicit and useful bounds on the output of the system, is also employed to determine the settling time. 相似文献
2.
This paper focuses on input-to-state stability of a class of switched stochastic delayed systems which are drived by Lévy noise. By multiple Lyapunov function and average dwell time approach, the sufficient conditions of the ψλ(t)-weighted input-to-state stability can be obtained if all the subsystems are input-to-state stable. Then utilizing comparison principle and the method of constant variation, the sufficient criteria of the eλt-weighted input-to-state stability of the switched stochastic delayed systems containing both input-to-state stable subsystems and non-input-to-state stable subsystems can also be derived. Finally, an example is given to illustrate the effectiveness of the proposed results. 相似文献
3.
In this paper, we use Leggett-Williams multiple fixed point theorem to obtain different sufficient conditions for the existence of at least three nonnegative periodic solutions of the first order functional differential equation of the form
y′(t)=-a(t)y(t)+λf(t,y(h(t))). 相似文献
4.
A method of using orthogonal shifted Legendre polynomials for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials is presented. It is based on the repeated integration of the differential equation and the representations of s(τ) dτ = Ps(t) and ts(t) = Rs(t), where P and R are constant matrices and s(t) is a shifted Legendre vector whose elements are shifted Legendre polynomials. The differential input-output equation is converted into a set of overdetermined linear algebraic equations for a least squares solution. The results of simulation studies are included to illustrate the applicability of the method. 相似文献
5.
Huaqing Li Hao Zhang Zheng Wang Yifan Zhu Qi Han 《Journal of The Franklin Institute》2019,356(6):3733-3761
This paper considers solving a class of optimization problems over a network of agents, in which the cost function is expressed as the sum of individual objectives of the agents. The underlying communication graph is assumed to be undirected and connected. A distributed algorithm in which agents employ time-varying and heterogeneous step-sizes is proposed by combining consensus of multi-agent systems with gradient tracking technique. The algorithm not only drives the agents’ iterates to a global and consensual minimizer but also finds the optimal value of the cost function. When the individual objectives are convex and smooth, we prove that the algorithm converges at a rate of if the homogeneous step-size does not exceed some upper bound, and it accelerates to O(1/t) if the homogeneous step-size is sufficiently small. When at least one of the individual objectives is strongly convex and all are smooth, we prove that the algorithm converges at a linear rate of O(λt) with 0?<?λ?<?1 even though the step-sizes are time-varying and heterogeneous. Two numerical examples are provided to demonstrate the efficiency of the proposed algorithm and to validate the theoretical findings. 相似文献
6.
In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments. 相似文献
7.
《Journal of The Franklin Institute》2021,358(15):7804-7824
This paper is concerned with the stability analysis of linear systems with time-varying delays. First, by introducing the quadratic terms of time-varying delays and some integral vectors, a more suitable Lyapunov-Krasovskii functional (LKF) is constructed. Second, two new delay-dependent estimation methods are developed in the stability analysis of linear system with time-varying delays, which include a reciprocally convex matrix inequality and an integral inequality. More information about time-varying delays and more free matrices are introduced into the two estimation approaches, which play a key role for obtaining an accurate upper bound of the integral terms in time derivative of LKFs. Third, based on the novel LKFs and new estimation approaches, some less conservative criteria are derived in the form of linear matrix inequality (LMI). Finally, three numerical examples are applied to verify the advantages and effectiveness of the newly proposed methods. 相似文献
8.
This paper improves stability criteria for neutral-type Lur’e systems with time-varying delays, where the nonlinearity satisfies sector and slope restrictions. A proposed Lyapunov–Krasovskii functional consisting of a quadratic term and integral terms for the time-varying delays and the nonlinearities, has four different characteristics. First, the quadratic term utilizes not only the current and delayed states but also the nonlinear vectors. Second, the integral terms for nonlinearities fully exploit the characteristics of sector and slope restrictions. Third, the integral terms for nonlinearities also exploit the characteristic of incremental restriction induced from the slope restriction. Fourth, this paper utilizes a vector related to the time derivative of the neutral delayed state to handle the neutral delay. Based on the proposed Lyapunov–Krasovskii functional, the improved stability criteria are derived in terms of linear matrix inequalities. Numerical examples show that the proposed criteria present less conservative results than the previous criteria. 相似文献
9.
《Journal of The Franklin Institute》2019,356(16):8996-9022
In this work, impulsive stabilization problems of discrete-time switched linear systems with time-varying delays are studied. The sequence of impulsive instants is nearly-periodic, i.e., it is close to a periodic impulse and the distance between them is an uncertain bounded term. A time-varying Lyapunov function is introduced to characterize the information of delays, switching signals and impulses, and a stability criterion LMI-based is obtained without any restrictions on the stability of the subsystems. Several design schemes of reduced-order/full-order impulsive controllers with or without time-varying delays are developed. Finally, three numerical examples are provided to illustrate the effectiveness of the established results. 相似文献
10.
Guy Jumarie 《Journal of The Franklin Institute》2010,347(10):1797-1813
The usual model for (Poissonian) linear birth-death processes is extended to multiple birth-death processes with fractional birth probabilities in the form λi(Δt)α+o((Δt)α, 0<α<1. The probability generating function for the time dependent population size is provided by a fractional partial differential equation. The solution of the latter is obtained and comparison with the usual model is made. The probability of ultimate extinction is obtained. One considers the special case of fractional Poissonian processes with individual arrivals only, and then one outlines basic results for continuous processes defined by fractional Poissonian noises. The key is the Taylor’s series of fractional order f(x+h)=Eα(hαDxα)f(x), where Eα(·) is the Mittag-Leffler function, and Dxα is the modified Riemann-Liouville fractional derivative, as previously introduced by the author. 相似文献
11.
This paper deals with the problems of robust delay-dependent stability and H∞ analysis for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, an improved delay-range-dependent stability condition for Markovian jump systems is proposed by constructing a novel Lyapunov-Krasovskii functional with the idea of partitioning the time delay, and a sufficient condition is derived from the H∞ performance. Numerical examples are provided to demonstrate efficiency and reduced conservatism of the results in this paper. 相似文献
12.
《Journal of The Franklin Institute》2014,351(12):5386-5398
In this paper, the problem of stability analysis for linear systems with time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, improved delay-dependent stability criteria for asymptotic stability of the system are proposed for two cases of conditions on time-varying delays with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via three numerical examples by the comparison of maximum delay bounds. 相似文献
13.
This paper focuses on the problem of robust H∞ filter design for uncertain systems with time-varying state and distributed delays. System uncertainties are considered as norm-bounded time-varying parametric uncertainties. The delays are assumed to be time-varying delays being differentiable uniformly bounded with delay-derivative bounded by a constant, which may be greater than one. A new delay-derivative-dependent approach of filter design for the systems is proposed. A novel Lyapunov-Krasovskii functional (LKF) is employed, and a tighter upper bound of its derivative is obtained by employing an inequality and using free-weighting matrices technique, then the proposed result has advantages over some existing results, in that it has less conservatism and it enlarges the application scope. An improved sufficient condition for the existence of such a filter is established in terms of linear matrix inequality (LMI). Finally, illustrative examples are given to show the effectiveness and reduced conservatism of the proposed method. 相似文献
14.
This paper is concerned with the robust stability of uncertain neutral-type Lur?e system with time-varying delays and sector bounded nonlinearities. By constructing a modified Lyapunov–Krasovskii functional (LKF), some new robust stability criteria are proposed in terms of linear matrix inequalities (LMIs) without using the general free-weighting matrix method. The criteria are less conservative and more efficiently calculative than some previous ones. Four numerical examples are presented to show the effectiveness and merits of the proposed approach. 相似文献
15.
This paper considers the stability and L2-gain for a class of switched neutral systems with time-varying discrete and neutral delays. Some new delay-dependent sufficient conditions for exponential stability and weighted L2-gain are developed for a class of switching signals with average dwell time. These conditions are formulated in terms of linear matrix inequalities (LMIs) and are derived by employing free weighting matrices method. As a special case of such switching signals, we can obtain exponential stability and normal L2-gain under arbitrary switching signals. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results. 相似文献
16.
Output feedback control of an uncertain input-delayed nonlinear system with bounded control commands
《Journal of The Franklin Institute》2022,359(12):6245-6266
This study focused on controlling a class of nonlinear systems with actuation time delays. We proposed a novel output-feedback controller in which the magnitude of the input commands is saturated and can be adjusted by varying control parameters. In this design, a predictor term is used to compensate for delays in the input, and auxiliary systems are exploited to provide a priori bounded control commands and account for the lack of full-state information. The stability analysis results revealed that uniformly ultimately bounded tracking is guaranteed despite modeling uncertainties and additive time-varying disturbances in the system dynamics. The performance of the controller was evaluated through simulation. 相似文献
17.
By means of Mawhin's continuation theorem, we study a third-order p-Laplacian differential equation
(?p(u″(t)))′+f(t,u′(t),u″(t))+g(t,u(t-τ(t)))=e(t). 相似文献
18.
Yong-Gui Kao Ji-Feng Guo Chang-Hong Wang Xi-Qian Sun 《Journal of The Franklin Institute》2012,349(6):1972-1988
This paper is devoted to investigating the robust stochastic exponential stability for reaction-diffusion Cohen–Grossberg neural networks (RDCGNNs) with Markovian jumping parameters and mixed delays. The parameter uncertainties are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Some criteria for delay-dependent robust exponential stability of RDCGNNs with Markovian jumping parameters are established in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing Matlab LMI toolbox. Numerical examples are provided to demonstrate the efficiency of the proposed results. 相似文献
19.
This paper deals with the problem of a new delay-dependent robust stability criteria for a class of mixed neutral and Lur’e systems. The system has time-varying uncertainties, interval time-varying delays and sector-bounded nonlinearity. The proposed method is based on Lyapunov method, a delay-dependent criterion for asymptotic stability is established in terms of linear matrix inequality (LMI). Numerical examples show the effectiveness of the proposed method. 相似文献
20.
Using Lu's continuation theorem, the extension one of Manásevich-Mawhin, we study the existence of periodic solutions for p-Laplacian neutral Liénard equation of the form
(?p(x(t)-cx(t-σ))′)′+f(x(t))x′(t)+β(t)g(x(t-τ(t))=e(t). 相似文献