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1.
This paper is concerned with the stability analysis of systems with two additive time-varying delay components in an improved delay interconnection Lyapunov–Krasovskii framework. At first, an augmented vector and some integral terms considering the additive delays information in a new way are introduced to the Lyapunov–Krasovskii functional (LKF), in which the information of the two upper bounds and the relationship between the two upper bounds and the upper bound of the total delay are both fully considered. Then, the obtained stability criterion shows advantage over the existing ones since not only an improved delay interconnection LKF is constructed but also some advanced techniques such as the free-matrix-based integral inequality and extended reciprocally convex matrix inequality are used to estimate the upper bound of the derivative of the proposed LKF. Finally, a numerical example is given to demonstrate the effectiveness and to show the superiority of the proposed method over existing results.  相似文献   

2.
This paper proposes an extended generalized integral inequality based on free matrices (EGIIFM) and applies it to the stability analysis of neural networks with time-varying delays. The EGIIFM estimates an upper bound for a quadratic form of a positive definite matrix with an augmented vector staked not only with the state and its derivative but also with the nonlinear activation function. By reflecting the correlated cross-information among the terms in the augmented vector as free matrices, the EGIIFM provides a tighter upper bound and encompasses various existing single integral inequalities as special cases. In addition, by establishing a new double integral Lyapunov–Krasovskii functional including the correlated cross-information, a less conservative stability criterion is obtained. Through three well-known numerical examples, the effectiveness of the EGIIFM is evaluated.  相似文献   

3.
This paper addresses the delay-dependent stability problem of linear systems with interval time-varying delays. A generalized free-matrix-based inequality is proposed and employed to derive stability conditions, which are less conservative than the Bessel–Legendre inequality. An augmented Lyapunov–Krasovskii functional is tailored for the generalized free-matrix-based inequality. Then, some items in the Lyapunov–Krasovskii functionals are integrated so as to relax its positive definite condition, which provides a more accurate lower bound for the Lyapunov–Krasovskii functionals. Therefore, some less conservative stability criteria are presented. Two numerical examples illustrate the effectiveness of the method.  相似文献   

4.
This paper deals with stability of discrete-time systems with an interval-like time-varying delay. By constructing a novel augmented Lyapunov functional and using an improved finite-sum inequality to deal with some sum-terms appearing in the forward difference of the Lyapunov functional, a less conservative stability criterion is obtained for the system under study if compared with some existing methods. Moreover, as a special case, the stability of discrete-time systems with a constant time delay is also investigated. Three numerical examples show that the derived stability criteria are less conservative and require relatively small number of decision variables.  相似文献   

5.
A new control design approach is proposed for a class of nonlinear systems expressed by Takagi–Sugeno (T-S) fuzzy model, considering several objectives including robustness against input time-varying delay, input constraint satisfaction, and reference tracking. The proposed controller is designed on the basis of an augmented model, Lyapunov–Krasovskii functional, linear matrix inequality (LMI) tools, and parallel distributed compensation (PDC) approach. Proof of the input-to-state stability (ISS) criterion is provided for the error dynamics. Input constraint satisfaction is performed using a reference-management algorithm based on the linearized closed-loop system from the reference input to the constrained variables. In order to illustrate the effectiveness of the proposed control approach, simulations are performed on three practical examples, including a flexible-joint robot and a continuous stirred tank reactor (CSTR).  相似文献   

6.
Novel stability criterion is presented for the existence, uniqueness and globally asymptotic stability of the equilibrium point of a class of cellular neural networks with time-varying delays. Based on Gu's discretized Lyapunov–Krasovskii functional (LKF) theory, a novel vector LKF is introduced by dividing the variation interval of the time delay into several subintervals with equal length. By using the homeomorphism mapping principle, free-weighting matrix method and linear matrix inequality (LMI) techniques, the obtained condition is less conservative than some previous results. Three examples are also given to show the effectiveness of the presented criterion.  相似文献   

7.
In this paper, we design observer-based feedback control for a class of linear systems. The novelty of the paper comes from the consideration of an augmented weighted based integral inequality involving quadratic functions with an exponential term which is less conservative than the celebrated weighted integral inequality employed in the context of time-delay systems. By using appropriately chosen Lyapunov–Krasovskii functional (LKF), together with the derived integral inequality, a new sufficient condition for exponential stability in terms of linear matrix inequalities (LMIs) is proposed for the delayed linear systems with state feedback control. Finally, the applicability and superiority of the proposed theoretical results over the existing ones are analyzed in virtue of numerical examples.  相似文献   

8.
This paper is concerned with the problem of delay-dependent stability for a class of singular time-delay systems. By representing the singular system as a neutral form, using an augmented Lyapunov–Krasovskii functional and the Wirtinger-based integral inequality method, we obtain a new stability criterion in terms of a linear matrix inequality (LMI). The criterion is applicable for the stability test of both singular time-delay systems and neutral systems with constant time delays. Illustrative examples show the effectiveness and merits of the method.  相似文献   

9.
This paper is concerned with the stability analysis of time-delay systems. Lyapunov–Krasovskii functional method is utilized to obtain stability criteria in the form of linear matrix inequalities. The main purpose is to obtain less conservative stability criteria by reducing the estimation gap of the time derivative of the constructed Lyapunov–Krasovskii functional. First, a generalized multiple-integral inequality is put forward based on Schur complement lemma. Then, some special cases of the proposed generalized multiple-integral inequality are given to estimate single and double integral terms in the derivative of Lyapunov–Krasovskii functional. Furthermore, less conservative stability criteria are derived. Finally, three examples are given to illustrate the improvement of the proposed criteria.  相似文献   

10.
This paper deals with the problem of non-fragile sampled-data stabilization analysis for a class of linear systems with probabilistic time-varying delays via new double integral inequality approach. Based on the auxiliary function-based integral inequality (AFBII) and with the help of some mathematical approaches, a new double integral inequality (NDII) is developed. Then, to demonstrate the merits of the proposed inequality, an appropriate Lyapunov–Krasovskii functional (LKF) is constructed with some augmented delay-dependent terms. By employing integral inequalities, an enhanced stability criterion for the concerned system model is derived in terms of linear matrix inequalities (LMIs). Finally, three benchmark illustrative examples are given to validate the effectiveness and advantages of the proposed results.  相似文献   

11.
The problem of the reachable set (RS) control of sliding mode control (SMC) for a class of singular systems with or without time-varying delay under zero initial conditions is studied. The purpose is to get an RS boundary containing all states of the system by designing an SMC. Firstly, singular systems with or without time-varying delay are decomposed into slow and fast subsystems by using the decomposition approach. Then, the augmented Lyapunov functional is built utilizing the decomposed state vector. The SMC is designed based on the exponential reaching criterion, resulting in the corresponding closed-loop control system (CLCS) construction. As a consequence, an RS criterion is constructed by employing the inequality scaling approach and the free-weighting matrix in conjunction with the linear matrix inequality (LMI). Finally, the validity and primacy of the results are provided by two numerical and practical examples.  相似文献   

12.
《Journal of The Franklin Institute》2019,356(18):11561-11580
This paper addresses the robust H∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results.  相似文献   

13.
This paper considers a stability analysis problem for continuous-time Markovian jump linear systems under aperiodic samplings which are represented as Markovian jump linear systems with input delay. For the systems, this paper constructs a Lyapunov functional by utilizing a fragmented-delay state, which is defined between the last sampling instant and the present time, and a new state space model of the fragmented state. Based on the Lyapunov functional, a stability criterion is derived in terms of linear matrix inequalities by using reciprocally convex approach and integral inequality. Here, the reciprocally convex approach and integral inequality are associated not only with the current state, the delayed state, and the maximum-admissible delay state, but also with the fragmented-delay state. The simulation result shows the effectiveness of the proposed stability criterion.  相似文献   

14.
This paper presents a new stability analysis of networked control systems (NCSs) with network-induced delay and packet dropout. A novel augmented Lyapunov–Krasovskii functional (LKF) is constructed, which takes into account the feature of the sawtooth delay induced by sample-and-hold. Based on an improved version of Wirtinger's inequality and the convex combination method, a delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). The advantage of the proposed criterion lies in its simplicity and less conservativeness than some of the existing results. The new criterion is applied to the network-based state feedback control problems. Numerical examples are given to verify the effectiveness of the proposed criterion.  相似文献   

15.
This paper is concerned with the problem of global robust asymptotic stability for delayed neural networks with polytopic parameter uncertainties and time-varying delay. A delay-dependent and parameter-dependent robust stability criterion for the equilibrium of delayed neural networks in the face of polytopic type uncertainties is presented by using a parameter-dependent Lyapunov functional and taking the relationship between the terms in the Leibniz–Newton formula into account. This criterion, expressed as a set of linear matrix inequalities, requires no matrix variable to be fixed for the entire uncertainty polytope, which produces a less conservative stability result.  相似文献   

16.
Competitive neural networks(CNNs) has not been well developed in nonlinear fractional order dynamical system, which is developed first time in this paper. Then, by means of a proper Lyapunov functional, asymptotic expansion of Mittag-Leffler function properties, together with some Caputo derivative properties, the testable novel sufficient conditions are given to guarantee the existence, uniqueness of the equilibrium point as well as global asymptotic stability for a class of fractional order competitive neural networks (FOCNNs) are all derived in the form of matrix elements. Furthermore, the boundedness for the solution of FOCNN is presented by employing Cauchy–Schwartz inequality and Gronwall inequality. Besides, a linear feedback control and adaptive feedback control are designed to achieve the global asymptotic synchronization criterion for FOCNNs with time delay and these explored consequences are extended from some previous integer order CNNs output. At last, two numerical simulations are performed to illustrate the effectiveness of our proposed theoretical results.  相似文献   

17.
This work investigates the improved stability conditions for linear systems with time-varying delays via various augmented approaches. Some augmented approaches are augmented Lyapunov-Krasovskii functionals, augmented zero equalities, and the augmented zero equality approach. At first, by constructing augmented Lyapunov-Krasovskii functionals including the state vectors which were not considered in the previous works and augmented zero equalities, a stability criterion is proposed in the forms of linear matrix inequalities. Through the proposed Lyapunov-Krasovskii functionals and an additional functional derived from the integral inequality, a slightly improved result is derived. The proposed results do not consider the increase in the computational complexity to achieve a larger delay bound. So, by applying the augmented zero equality approach, which is a method of grafting the proposed augmented zero equality proposed in Finsler Lemma, to the proposed result, an enhanced stability result was derived. Also, the computational complexity is reduced by appropriately adjusting any vector of the integral inequality utilized in the proposed criteria. By applying some numerical examples to the proposed conditions, the effectiveness and superiority of the results are confirmed.  相似文献   

18.
In this paper, we intend to discuss the passivity of coupled neural networks (NNs) with reaction–diffusion terms and mixed delays. By constructing appropriate Lyapunov functional, and with the help of liner matrix inequalities, some inequality techniques, several sufficient conditions are derived to guarantee the output strictly passive, input strictly passive, passive of the proposed neural network model. Then, a stability criterion is presented according to the obtained passivity results. Moreover, the proposed neural network model herein is more general than some recent studies, which can improve and enrich the previous research results. Finally, a numerical example is presented to show the effectiveness of the theoretical criteria.  相似文献   

19.
This paper is concerned with the problem of robust synchronization of a class of complex dynamical networks with time-varying delays and reaction–diffusion terms. To reflect most of the dynamical behaviors of the system, the parameter uncertainties are considered. A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. The control objective is that the trajectories of the system by designing suitable control schemes track the trajectories of the system with sample-data control. It is shown that, through Lyapunov stability theory, the proposed sample-data controllers are successful in ensuring the achievement of robust synchronization of complex dynamical networks even in the case of uncertainity and Markovian jumping parameters. By utilizing the Lyapunov functional method, Jensen’s inequality, Wirtinger’s inequality and lower bounds theorem, we establish a sufficient criterion such that, for all admissible parameter uncertainties, the complex dynamical network is robustly synchronized. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.  相似文献   

20.
This paper is concerned with the problem of delayed proportional-integral control of an offshore platform subject to self-excited nonlinear hydrodynamic force. By using current and distributed delayed states, a delayed proportional-integral controller is designed to stabilize the offshore platform. Under such a controller, the closed-loop system of the offshore platform is modeled as a nonlinear system with discrete and distributed delays, which allows us to employ the Lyapnov–Krasovskii functional method to analyze its asymptotic stability. Since an affine Wirtinger-based inequality is exploited to estimate the derivative of the Lyapunov–Krasovskii functional, a new stability criterion for the closed-loop system is derived, based on which, suitable control gains can be designed provided that a set of linear matrix inequalities are feasible. It is found through simulation results that the proposed control scheme can improve the control performance remarkably. Moreover, (i) compared with the existing delay-free controllers, the proposed controller can reduce the required control force and the oscillation amplitudes of the platform significantly; and (ii) compared with several delayed controllers, the proposed controller requires less control cost.  相似文献   

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