带有非线性扰动的时变时滞系统的稳定性准则

研究了带有非线性扰动的时变时滞系统的稳定性问题.基于时滞分割方法,提出了保守性更小的系统稳定性分析准则.利用一个自由参数将时滞区间分割为2个子区间,进而构造了含有时滞分割点状态信息和3重积分项的Lyapunov-Krasovskii泛函,并采用自由矩阵积分不等式界定泛函导数中的交叉项.基于Lyapunov稳定性定理,得到了以线性矩阵不等式描述的时滞相关型稳定性准则.数值算例表明该稳定性准则能够得到更大的时滞上界,与已有结果相比具有更小的保守性.     

New criteria for exponential stability of nonlinear difference systems with time-varying delay

General nonlinear time-varying difference systems with time-varying delay are considered. Some new explicit criteria for global exponential stability are given. Two examples are given to illustrate the obtained results.     

Delay-range-dependent stability for uncertain stochastic systems with interval time-varying delay and nonlinear perturbations

This paper considers the problem of robust stability for a class of uncertain stochastic systems with interval time-varying delay under nonlinear perturbations. A new delay-dependent method for robust stability of the systems is proposed. The innovation of the method includes employment of a tighter integral inequality and construction of an appropriate type of Lyapunov–Krasovskii functional. The restriction used to bound some trace term in the existing methods is also removed. The resulting criterion derived from this method has advantages over previous ones in that it has less conservatism and enlarges the scope of application. The reduction in conservatism of the proposed criterion is attributed to a method to estimate the upper bound on the stochastic differential of the Lyapunov–Krasovskii functional without neglecting any useful terms in the delay-dependent stability analysis. On the basis of the estimation and by utilizing free-weighting matrices, new delay-range-dependent stability criterion is established in terms of linear matrix inequality. Finally, numerical examples are provided to show the effectiveness and reduced conservatism of the proposed method.     

Simple stability criteria for nonlinear time-varying discrete systems

We present two sufficient conditions for asymptotic stability of nonlinear time-varying discrete systems. Our main results generalize Mori's result for linear discrete time-invariant systems to nonlinear time-varying systems.     

New stability criteria of linear singular systems with time-varying delay

Most of the existing results on the stability problem of delayed singular systems only pertain to the case of constant delay. This is due to the fact that time-varying delay makes it hardly possible to explicitly express the fast variables. In this paper, aiming at dealing with the case of time-varying delay, we create a way to prove the stability by using a perturbation approach. Rather, we first get the decay rate for slow variables by using Lyapunov functional approach and, furthermore, guarantee that the fast variables fall into decay by characterising their effect on the derived decay rate. Also, we present a convexity technique in computing the constructed Lyapunov functional which contributes to the elimination of the possible conservatism caused by the varying rate of delay. Finally, we provide two numerical examples to demonstrate the effectiveness of the method.     

New stability criteria of singular systems with time-varying delay via free-matrix-based integral inequality

This paper concerns the stability problem of singular systems with time-varying delay. First, the singular system with time-varying delay is transformed into the neutral system with time-varying delay. Second, a more proper Lyapunov–Krasovskii functional (LKF) is constructed by adding some integral terms to quadratic forms. Then, to obtain less conservative conditions, the free-matrix-based integral inequality is adopted to estimate the derivative of LKF. As a result, some delay-dependent stability criteria are given in terms of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method.     

带非线性扰动的不确定多时变时滞系统H∞鲁棒稳定性

研究了带非线性扰动的不确定多时变时滞系统的H∞鲁棒稳定性．其中不确定项是范数有界的,非线性扰动满足线性约束．基于Lyapunov-Krasovskii泛函,根据矩阵不等式技术和非线性处理方法,提出了两个新的时滞稳定性的结果．最后给出了两个示例,表明本文提出的方法与存在的文献结果相比,具有较少的保守性和良好的有效性．     

New delay-dependent absolute stability criteria for Lur'e systems with time-varying delay

In this article, the absolute stability problem is investigated for Lur'e systems with time-varying delay and sector-bounded nonlinearity. By employing the delay fractioning idea, the new augmented Lyapunov functional is first constructed. Then, by introducing some slack matrices and by reserving the useful term when estimating the upper bound of the derivative of Lyapunov functional, the new delay-dependent absolute stability criteria are derived in terms of linear matrix inequalities. Several numerical examples are presented to show the effectiveness and the less conservativeness of the proposed method.     

Finite-time stability and stabilisation of singular discrete-time linear positive systems with time-varying delay

ABSTRACT

In this paper, the problem of finite-time stability and stabilisation for positive singular discrete-time linear systems with time-varying delay is investigated. We first present novel delay-dependent sufficient conditions for positivity and finite-time stability of the unforced systems. We then apply the obtained results to solve finite-time stabilisation problem of the considered systems. The sufficient conditions for the positivity and finite-time stabilisable of such systems are formulated in terms of a standard linear programming (LP) problem. Numerical examples are provided to illustrate the effectiveness and advantages of our results.     

Less conservative robust stability criteria for uncertain discrete stochastic singular systems with time-varying delay

The problem of robust stabilisation for uncertain discrete singular systems with time-varying delay is discussed in this article. First, a new delay-distribution-dependent Lyapunov function is established. Then, sufficient conditions are proposed for guaranteeing that the uncertain discrete singular system with time-varying delay has the properties of regularity, causality and stability. Finally, a suitable robust state feedback controller is designed by linear matrix inequality. Numerical examples illustrate that the results derived from the proposed method are less conservative than the existing ones.     

非线性时滞奇异系统的严格实用稳定性研究

将严格实用稳定性相关概念推广到具有控制输入的非线性奇异系统,利用两个Lyapunov函数方法和比较原理,得出其严格实用稳定及严格实用渐近稳定的判别准则.另外,我们给出了含有时滞的非线性奇异系统关于两个测度严格实用稳定的定义,并得出该类系统严格实用稳定及严格实用渐近稳定的充分条件.     

Delay-dependent criteria for robust stability of linear neutral systems with time-varying delay and nonlinear perturbations

This article investigates the robust stability of linear neutral systems with time-varying delay and nonlinear perturbations. Using a new Lyapunov–Krasovskii functional and employing some free weighting matrices, less conservative delay-dependent robust stability conditions for such systems in terms of linear matrix inequalities are derived. Numerical examples are given to indicate significant improvements over some existing results.     

Delay-range-dependent stability criterion for interval time-delay systems with nonlinear perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii (LK) functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality (LMI) framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.     

Switched nonlinear singular systems with time‐delay: Stability analysis

This paper presents an approach to the stability analysis of a class of nonlinear interconnected continuous‐time singular systems with arbitrary switching signals. This class of interconnected subsystems consists of unknown but bounded state delay and nonlinear terms, and each subsystem can be globally stable, unstable, or locally stable. By constructing a new Lyapunov‐like Krasovskii functional, sufficient conditions are derived and formulated to check the asymptotic (exponential) stability of such systems with arbitrary switching signals. Then, some new general criteria for asymptotic (exponential) stability with average dwell‐time switching signals are also established. The theoretical developments are demonstrated by two numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

改进的时变时滞中立型系统的绝对稳定性判据

研究具有时变时滞和扇区有界非线性的中立型系统的绝对稳定性问题.根据时变时滞分段分析思想,构造一个新的Lyapunov-Krasovskii泛函,得到了一些保守性更小的基于线性矩阵不等式的时滞相关绝对稳定性判据.采用凸组合方法,可以避免忽略Lyapunov-Krasovskii泛函微分中的有用项.数值算例表明了所提出方法的有效性.     

Stability analysis of hybrid switched nonlinear singular time-delay systems with stable and unstable subsystems

The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.     

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the e?ectiveness of the proposed approach.     

时变时滞离散广义Markov 跳变系统的鲁棒稳定性

研究一类具有区间时变时滞的离散不确定广义Markov跳变系统的时滞相关鲁棒稳定性问题.通过将Jensen不等式与一个新的定界不等式相结合,得到了一个新的稳定性判据,该判据中仅含有Lyapunov变量,具有较小的计算负担.进而,基于凸组合方法得到了另一个新的稳定性判据,该判据引入了一些自由矩阵变量,具有较小的保守性.数值算例表明了所提出方法的有效性.     

Robustness of stability of nonlinear systems with stochastic delay perturbations

Suppose there exist random disturbances to a given exponentially stable system and the stochastically perturbed system is described by a stochastic differential-functional equation. In this paper a sufficient condition is given so that the perturbed system remains exponentially stable. In the case where the perturbation depends only on several states of the past we obtain a condition under which the perturbed system is absolutely exponentially stable.