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1.
This paper is concerned with the problems of finite-time boundedness and finite-time control for positive coupled differential-difference equations (CDDEs) with bounded time-varying delay. The finite-time stability of such systems is analyzed by constructing an estimate of the solutions over a finite time interval. And, sufficient conditions based on linear programming (LP) are provided for finite-time stability of positive CDDEs with bounded time-varying delay. Then, by coordinate transformation, the obtained results are extended to the finite-time bounedness of positive CDDEs with bounded time-varying delay. By the obtained result of finite-time boundedness, static output-feedback controllers and static state-feedback controllers are designed and a sufficient condition is derived to ensure the positivity and finite-time boundedness of closed-loop system. Three illustrative examples are given to show the validity of our results.  相似文献   

2.
This paper is concerned with the problems of set-based finite-time stability (SFTS) and set-based finite-time boundedness (SFTB) for both certain and uncertain linear time-varying systems. The concepts of SFTS and SFTB are defined. Different from existing results, sufficient conditions for SFTS and SFTB are directly derived from the basic definitions of finite-time stability (FTS) and finite-time boundedness (FTB) by using the convex hull technique rather than utilizing the weighted quadratic functions. Thus, more practical constraints on the system states can be dealt with. Furthermore, intervals, zonotopes and polytopes are employed to describe the typical compact convex sets. For linear uncertain systems, the uncertain time-varying state sets are assumed to be represented by interval matrices and matrix zonotopes, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the main results.  相似文献   

3.
This paper gives some Razumikhin-type theorems on pth moment boundedness of stochastic functional differential equations with Markovian switching (SFDEwMS) by using Razumikhin technique and comparison principle. Some improved conditions on pth moment stability are also proposed. The main results of this paper allow the estimated upper bound of the diffusion operator associated with the underlying SFDEwMS of the Lyapunov function to have time-varying coefficients (the coefficients may even be sign-changing functions). Examples are provided to illustrate the effectiveness of the proposed results.  相似文献   

4.
The main results of the paper are improvements on the stability analysis of Halanay inequalities with time-varying coefficients in both continuous-time and discrete-time setting. Three classes of improved conditions are established to ensure that the solution to the Halanay inequality is uniformly exponentially stable. The merit of the proposed new conditions is that the coefficients of the Halanay inequality can be unbounded and sign indefinite. This is achieved by using the notion and properties of uniformly asymptotic stable (UAS) functions. Based on the improved stability conditions for the Halanay inequality and the Lyapunov Razumikhin approach, three classes of sufficient conditions are established for testing the stability of time-varying time-delay systems. Finally, the advantages of the proposed methods are illustrated by some numerical examples with some of them borrowed from the literature.  相似文献   

5.
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6.
This paper discusses the problems of delay-dependent stability and stabilization of neutral saturating actuator systems with constant or time-varying delays. The problems of stabilization for neutral saturating actuator system with time-varying delay and parameter from the presented results, the condition obtained here does not need derivative information of the delay time and thus can be used to analyze the stabilization problem for a class of saturating actuator systems with time-varying delay, which is bounded but arbitrarily fast time-varying. Using the model transformation and quasi-convex optimization problem, we derive delay-dependent conditions for the stability of systems in terms of the linear matrix inequality. The stabilization conditions are formulated as linear matrix inequalities (LMIs) which can be solved by convex optimization algorithm. Moreover, the stability criteria are extended to design a stabilizing state feedback controller. Numerical examples show that the results obtained in this paper significantly improve the estimate of stability limit over some existing results reported previously in the literature.  相似文献   

7.
This paper is concerned with the issue of finite-time boundedness of discrete-time uncertain interval type-2 fuzzy systems with time-varying delay and external disturbances via an observer-based reliable control strategy. According to the system output variable, a full-state observer that shares the same membership functions of the plant is constructed to estimate the unknown system states. In addition, a reliable controller subject to observer states and actuator faults is designed to formulate the closed-loop feedback control system, which does not share the same membership functions of the plant. Then, by constructing an appropriate Lyapunov–Krasovskii functional and using the finite-time stability theory, a new set of delay-dependent sufficient conditions guaranteeing the finite-time boundedness of the addressed system is established in the framework of linear matrix inequalities. Furthermore, the explicit expressions of gain matrices of the state observer and the reliable controller are given in terms of the established sufficient conditions. Finally, simulation results are presented to demonstrate the effectiveness of the obtained theoretical results.  相似文献   

8.
In this paper, the global exponential robust stability is investigated for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms, this neural network contains time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. Neither the boundedness and differentiability on the activation functions nor the differentiability on the time-varying delays are assumed. By using general Halanay inequality and M-matrix theory, several new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential robust stability of equilibrium point for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms. Several previous results are improved and generalized, and three examples are given to show the effectiveness of the obtained results.  相似文献   

9.
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.  相似文献   

10.
A control scheme based on dynamic gains is proposed for the time-varying nonlinear time-delay systems with unknown control coefficients. A class of Nussbaum functions are introduced to deal with the problem of unknown control directions. Dynamic gains technique and Lyapunov–Krasovskii functional are developed to handle the time delays in nonlinear system. It is shown that the system state is regulated to origin asymptotically, and the boundedness of all closed-loop signals is guaranteed. Simulation results are provided to demonstrate the effectiveness of the proposed methodology.  相似文献   

11.
The problem of finite-time stability for linear discrete-time systems with time-varying delay is studied in this paper. In order to deal with the time delay, the original system is firstly transformed into two interconnected subsystems. By constructing a delay-dependent Lyapunov–Krasovskii functional and using a two-term approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Compared with the existing results on finite-time stability, the derived stability conditions are less conservative. In addition, for the stabilization problem, we design the state-feedback controller. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.  相似文献   

12.
This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods.  相似文献   

13.
The primary goal of this paper is to examine the finite-time stability and finite-time contractive stability of the linear systems in fractional domain with time-varying delays. We develop some sufficient criteria for finite-time contractive stability and finite-time stability utilizing fractional-order Lyapunov-Razumikhin technique. To validate the proposed conditions, two different types of dynamical systems are taken into account, one is general time-delay fractional-order system and another one is fractional-order linear time-varying time-delay system, furthermore the efficacy of the stability conditions is demonstrated numerically.  相似文献   

14.
This paper tackles a distributed hybrid affine formation control (HAFC) problem for Euler–Lagrange multi-agent systems with modelling uncertainties using full-state feedback in both time-varying and constant formation cases. First, a novel two-layer framework is adopted to define the HAFC problem. Using the property of the affine transformation, we present the sufficient and necessary conditions of achieving the affine localizability. Because only parts of the leaders and followers can access to the desired formation information and states of the dynamic leaders, respectively, we design a distributed finite-time sliding-mode estimator to acquire the desired position, velocity, and acceleration of each agent. In the sequel, combined with the integral barrier Lyapunov functions, we propose a distributed formation control law for each leader in the first layer and a distributed affine formation control protocol for each follower in the second layer respectively with bounded velocities for all agents, meanwhile the adaptive neural networks are applied to compensate the model uncertainties. The uniform ultimate boundedness of all the tracking errors can be guaranteed by Lyapunov stability theory. Finally, corresponding simulations are carried out to verify the theoretical results and demonstrate that with the proposed control approach the agents can accurately and continuously track the given references.  相似文献   

15.
This paper is concerned with robust stability analysis of second-order linear time-varying (SLTV) systems with time-varying uncertainties (perturbations). With the specific Lyapunov functions, a simple and neat algebraic criterion for testing uniformly asymptotic stability of SLTV systems are derived. Without transformation to a system of first-order equations, the new conditions are imposed directly on the time-varying coefficient matrices of the system. The main feature of the proposed algebraic criterion is that the uncertain coefficient matrices are time-varying and not necessarily symmetric. Finally, the proposed stability conditions are used to design the extending space structures system of the spacecraft. Simulation results are provided to illustrate the convenience and effectiveness of the proposed method.  相似文献   

16.
Most temporal signals of practical interest are nonstationary and need to be modeled using time-varying systems. In this paper a composite model for these signals is proposed which accounts for nonstationarities in the mean and the autocorrelation functions. Unbiased and consistent time-varying estimators for the mean and the variance functions are studied and used to produce zero-mean, constant-variance signals that can be modeled using autoregressive systems with time-varying coefficients. The identification of the coefficients is implemented recursively using the parameterization of the coefficients by a set of basis functions. We illustrate the application of the composite model in the analysis and synthesis of speech and in the estimation of instantaneous frequencies in radar return signals.  相似文献   

17.
In this paper, we study a distributed state estimation problem for Markov jump systems (MJS) over sensor networks, in which each sensor node connects with each other through wireless networks with communication delays. We assume that each sensor node maintains a buffer to store delayed data transmitted from neighbor nodes. A distributed multiple model filter is designed by using the interacting multiple model methods (IMM) and a recursive delays compensation method. In order to ensure the stability, two stability conditions are derived for boundedness of estimation errors and boundedness of error covariance. Finally, the effectiveness of the proposed methods is illustrated by simulations and experiments of maneuvering target tracking.  相似文献   

18.
This paper presents new exponential stability and stabilization conditions for a class of uncertain linear time-delay systems. The unknown norm-bounded uncertainties and the delays are time-varying. Based on an improved Lyapunov-Krasovskii functional combined with Leibniz-Newton formula, the robust stability conditions are derived in terms of linear matrix inequalities (LMIs), which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. The result can be extended to uncertain systems with time-varying multiple delays. The effectiveness of the two stability bounds and the reduced conservatism of the conditions are shown by numerical examples.  相似文献   

19.
In this paper, a new memory-based control problem is addressed for neutral systems with time-varying delay, input saturations and energy bounded disturbances. Attention is focused on the design of a memory-based state feedback controller such that the closed-loop system achieves the desirable performance indices including the boundedness of the state trajectories, the H∞ disturbance rejection/attenuation level as well as the asymptotic stability. By using the combination of a novel delay-dependent polytopic approach, augmented Lyapunov–Krasovskii functionals and some integral inequalities, delay-dependent sufficient conditions are first proposed in terms of linear matrix inequalities. Then, three convex optimization problems are formulated whose aims are to, respectively, maximize the disturbance tolerance level, minimize the disturbance attenuation level and maximize the initial condition set. Finally, simulation examples demonstrate the effectiveness and benefits of the obtained results.  相似文献   

20.
In this note, we will devote to investigate the stability of discrete-time switched positive linear time-varying systems (PLTVSs). Firstly, a new asymptotic stability criterion of discrete-time PLTVSs is obtained by using time-varying copositive Lyapunov functions (TVCLFs) and this criterion is then extended to the switched case based on the multiple TVCLFs. Furthermore, the sufficient conditions are derived for stability of discrete-time switched PLTVSs with stable subsystems by means of function-dependent average dwell time and function-dependent minimum dwell time. In addition, the stability sufficient conditions are drawn for the switched PLTVSs which contain unstable subsystems. It is worth noting that the difference of TVCLFs and multiple TVCLFs are both relaxed to indefinite in our work. The theoretical results obtained are verified by two numerical examples.  相似文献   

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