Robust stability criteria for uncertain linear systems with interval time-varying delay

This paper considers the robust delay-dependent stability problem of a class of linear uncertain system with interval time-varying delay and proposes less conservative stability criteria for computing the maximum allowable bound of the delay range. Less conservatism of the proposed stability criteria is attributed to the delay-central point method of stability analysis, wherein the delay interval is partitioned into two subintervals of equal length, and the time derivative of a candidate Lyapunov-Krasovskii functional based on delay decomposition technique is evaluated in each of these delay segments. In deriving the stability conditions in LMI framework, neither model transformations nor bounding techniques using free-weighting matrix variables are employed for dealing the cross-terms that emerge from the time derivative of the Lyapunov-Krasovskii functional; instead, they are dealt using tighter integral inequalities. The proposed analysis subsequently yields a stability condition in convex LMI framework that can be solved using standard numerical packages. For deriving robust stability conditions, two categories of system uncertainties, namely, time-varying structured and polytopic-type uncertainties, are considered. The effectiveness of the proposed stability criteria is validated through standard numerical examples.     

Delay-dependent robust H-infinity filtering for uncertain linear systems with time-varying interval delay

This paper proposed a design method for delay-dependent robust H-infinity filter of linear systems with uncertainty and time-varying interval delay.The proposed method was shown to be much simpler than existing ones while giving significant improvement to the existing results.The key step in the method was to construct a special type of Lyapunov functional for the filter design problem.Unlike the existing techniques,the proposed method employed neither free weighting matrices nor any model transformation,le...     

On control for linear systems with interval time-varying delay

This paper deals with the problem of delay-dependent robust H_∞ control for linear time-delay systems with norm-bounded, and possibly time-varying, uncertainty. The time-delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available, and no restriction on the derivative of the time-varying delay is needed, which allows the time-delay to be a fast time-varying function. Based on an integral inequality, which is introduced in this paper, and Lyapunov–Krasovskii functional approach, a delay-dependent bounded real lemma (BRL) is first established without using model transformation and bounding techniques on the related cross product terms. Then employing the obtained BRL, a delay-dependent condition for the existence of a state feedback controller, which ensures asymptotic stability and a prescribed H_∞ performance level of the closed-loop systems for all admissible uncertainties, is proposed in terms of a linear matrix inequality (LMI). A numerical example is also given to illustrate the effectiveness of the proposed method.     

Improved results for linear discrete-time systems with an interval time-varying input delay

This paper addresses the problem of delay-dependent stability analysis and controller synthesis for a discrete-time system with an interval time-varying input delay. By dividing delay interval into multiple parts and constructing a novel piecewise Lyapunov–Krasovskii functional, an improved delay-partitioning-dependent stability criterion and a stabilisation criterion are obtained in terms of matrix inequalities. Compared with some existing results, since a tighter bounding inequality is employed to deal with the integral items, our results depend on less number of linear matrix inequality scalar decision variables while obtaining same or better allowable upper delay bound. Numerical examples show the effectiveness of the proposed method.     

Delay-range-dependent stability for systems with time-varying delay

This paper is concerned with the stability analysis for systems with time-varying delay in a range. An appropriate type of Lyapunov functionals is proposed to investigate the delay-range-dependent stability problem. The present results may improve the existing ones due to a method to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed Lyapunov functional, which take into account the range of delay. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.     

含区间时变时滞的线性不确定系统鲁棒稳定性新判据

研究一类区间时变时滞线性不确定系统的鲁棒稳定性问题.通过引入增广Lyapunov泛函,结合积分不等式方法,导出了区间时变时滞线性系统的时滞相关鲁棒稳定性新判据.与现有方法不同,该方法不涉及自由权矩阵技术和任何模型变换,减少了理论和计算上的复杂性,而且在估计Lyapunov泛函导数的上界时没有忽略某些有用项.数值算例表明,所提出的判据是有效的,具有更低的保守性.     

Robust stability for uncertain genetic regulatory networks with interval time-varying delays

This paper addresses the problem of robust stability of uncertain genetic regulatory networks (GRNs) with interval time-varying delays. We derive some new delay-range-dependent and delay-derivative-dependent/independent stability criteria by employing some free-weighting matrices and linear matrix inequalities. In our analysis, we carefully consider the relationship between the time-varying state delays and their bounds when calculating the upper bound of the derivative of Lyapunov functional. We hence show that, the rigorous requirement of other literatures that the time-derivatives of time-varying delays must be smaller than one is abandoned in the proposed scheme. The new criteria are applicable to both fast and slow time-varying delays. Finally, four numerical examples are presented to illustrate the effectiveness and the less conservativeness of the developed results.     

Delay-dependent exponential stability for uncertain neutral stochastic neural networks with interval time-varying delay

This paper is mainly concerned with the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic neural networks with interval time-varying delay. With an appropriate augmented Lyapunov–Krasovskii functional (LKF) formulated, the convex combination method is utilised to estimate the derivative of the LKF. Some new delay-dependent exponential stability criteria for such systems are obtained in terms of linear matrix inequalities, which involve fewer matrix variables and have less conservatism. Finally, two illustrative numerical examples are given to show the effectiveness of our obtained results.     

Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays

This paper is concerned with the robust asymptotic stability analysis for uncertain genetic regulatory networks with both interval time-varying delays and stochastic noise. By using the stochastic analysis approach, employing some free-weighting matrices and introducing an appropriate type of Lyapunov functional which takes into account the ranges of delays, some new delay-range-dependent and rate-dependent stability criteria are established in terms of linear matrix inequalities (LMIs) to guarantee the delayed genetic regulatory networks to be robustly asymptotically stable in the mean square. As a result, the new criteria are applicable to both fast and slow time-varying delays. Five numerical examples are also used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.     

A delay-dependent passivity criterion of linear neutral delay systems

The problem of delay-dependent stability and passivity for linear neutral systems is discussed. By constructing a novel type Lyapunov-krasovskii functional, a new delay-dependent passivity criterion is presented in terms of linear matrix inequalities （LMIs）. Model transformation, bounding for cross terms and selecting free weighting matrices [12-14] are not required in the arguments. Numerical examples show that the proposed criteria are available and less conservative than existing results .     

Delay-dependent robust stability for uncertain linear systems with interval time-varying delay

This paper is concerned with the delay-dependent robust stability problem for uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and no restriction on the derivative of the time-varying delay is needed, which allows the delay to be a fast time-varying function. The uncertainty under consideration is norm-bounded, and possibly time-varying, uncertainty. Based on the Lyapunov-Krasovskii functional approach, a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria. Numerical examples are given to demonstrate effectiveness of the proposed method.     

Reliable Memory Feedback Design for a Class of Nonlinear Fuzzy Systems with Time-varying Delay

This paper is concerned with the robust reliable memory controller design for a class of fuzzy uncertain systems with time-varying delay. The system under consideration is more general than those in other existent works. The controller, which is dependent on the magnitudes and derivative of the delay, is proposed in terms of linear matrix inequality (LMI). The closed-loop system is asymptotically stable for all admissible uncertainties as well as actuator faults. A numerical example is presented for illustration.     

一类区间时变输入时滞与状态时滞线性系统的稳定性研究

研究一类具有区间时变输入时滞与状态时滞线性系统的稳定性问题．通过选择合理的ＬｙａｐｕｎｏｖＫｒａｓｏｖｓｋｉｉ函数,基于积分等式方法（积分等式由自由权矩阵构造而成）,以ＬＭＩ的形式给出时滞相关的稳定性充分条件,并进行了相关控制器的设计．所得结论对时滞导数没有任何限制,可用于快时变时滞系统．同时,积分等式方法较积分不等式方法更优,保守性更低．最后,通过数值比较及仿真表明了所提出方法的有效性和优越性．     

Robust static output feedback control for linear discrete-time systems with time-varying uncertainties

This paper is concerned with the problem of designing robust static output feedback controllers for linear discrete-time systems with time-varying polytopic uncertainties. Sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities, and the results are extended to H₂ and H_∞ static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.     

Improved delay-range-dependent stability criteria for linear systems with time-varying delays

This paper is concerned with the stability analysis of linear systems with time-varying delays in a given range. A new type of augmented Lyapunov functional is proposed which contains some triple-integral terms. In the proposed Lyapunov functional, the information on the lower bound of the delay is fully exploited. Some new stability criteria are derived in terms of linear matrix inequalities without introducing any free-weighting matrices. Numerical examples are given to illustrate the effectiveness of the proposed method.     

Stability analysis for recurrent neural networks with time-varying delay

This paper is concerned with the stability analysis for static recurrent neural networks （RNNs） with time-varying delay. By Lyapunov functional method and linear matrix inequality technique, some new delay-dependent conditions are established to ensure the asymptotic stability of the neural network. Expressed in linear matrix inequalities （LMIs）, the proposed delay-dependent stability conditions can be checked using the recently developed algorithms. A numerical example is given to show that the obtained conditions can provide less conservative results than some existing ones.     

Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems

In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback controller synthesis. In stark contrast with existing approaches that are confined to memoryless static controller synthesis, we explore dynamical controller synthesis and reveal a particular periodically time-varying memory state-feedback controller (PTVMSFC) structure that allows LMI-based synthesis. In the context of robust controller synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static controller synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is “exact” in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.     

New robust exponential stability analysis for uncertain neural networks with time-varying delay

In this paper, the global robust exponential stability is considered for a class of neural networks with parametric uncer-tainties and time-varying delay. By using Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional, some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are presented to show the effectiveness of the proposed method.     

一类状态及输入均有区间变时滞的线性系统之镇定

对一类同时具有状态和输入变时滞的线性系统(x)(t)=Ax(t) A1x(t-τ1(t)) B1u(t) B2υ(t-τ2(t)),利用一种时滞划分形式的Lyapunov-Krasovskii泛函讨论其镇定问题.得到通过状态反馈控制使闭环系统稳定的时滞相关的镇定准则.对(A,B1)和(A A1,B1)都不可控的数值实例,利用本文给出的准则都能得到有效的控制.     

New stability criteria for linear systems with interval time-varying delay

This paper investigates robust stability of uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. A new Lyapunov-Krasovskii functional, which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to drive some new delay-dependent stability criteria. In order to obtain much less conservative results, a tighter bounding for some term is estimated. Moreover, no redundant matrix variable is introduced. Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.