一类线性时滞系统的鲁棒稳定性分析

针对一类具有范数有界不确定性和2个继发时变时滞的线性时滞不确定系统,研究了其时滞依赖鲁棒稳定性问题.通过定义充分利用时变时滞上下界信息的新型Lyapunov-Krasovskii泛函,并结合时滞系统相关处理方法和线性矩阵不等式方法,得到了时滞线性不确定系统鲁棒渐近稳定所满足的条件.为了降低结论的保守性,对某些项进行了较紧致的估计.此外,并未引入自由权矩阵.最后并通过2个数值仿真证实了方法的有效性和优越性.     

Delay-Dependent Robust Stability Criteria for Two Classes of Uncertain Singular Time-Delay Systems

In this note, the delay-dependent robust stability criteria for two classes of singular time-delay systems with norm-bounded uncertainties are investigated. First, without using model transformation and bounding technique for cross terms, an improved delay-dependent stability criterion for the nominal singular time-delay system is established in terms of strict linear matrix inequalities (LMIs). Then, based on this criterion, the delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems are proposed, which ensure that the systems are regular, impulse free and asymptotically stable for all admissible uncertainties. Numerical examples are proposed to illustrate the less conservatism of the obtained results     

Robust stability analysis of singular linear system with delay and parameter uncertainty

1Introduction It is well known that the existence of a delay in adynamical system may induce instability or poorperformances in various systems suchas electric,pneumatic,and hydraulic networks,chemical processes,longtransmission lines,etc.For a survey of time_delay systems,the reader can refer to a recent overview paper[1].Control of singular systems has been extensively studied inthe past years due to the fact that singular systems betterdescribe physical systems than regular ones.Agreat numb…     

Robust stability analysis of singular linear system with delay and parameter uncertainty

This paper deals with th e problem of robust stability for continuous-time sin gular systems with state delay and parameter uncerta inty.The uncertain singular systems with delay consi dered in this paper are assumed to be regular and impulse free.By decomposing the systems into slow and fast subsystems,a robust delay-dependent asymptotic stability criteria based on linear matrix inequality is proposed,which is derived by using Lyapunov-Krasovskii functionals,neither model transformatio n nor bounding for cross terms is required in the derivation of our delay-dependent result.The r obust delay-dependent stability criterion proposed in th is paper is a sufficient condition.Finally,numerical examples and Matlab simulation are provided to illustrate the effectiveness of the proposed method.     

具有时变时滞的Lurie系统时滞依赖绝对稳定性新判据

考虑了一类具有时变时滞和范数有界不确定的Lurie控制系统绝对稳定性分析问题. 通过选取一个新的Lyapunov-Krasovskii泛函将整个时滞区间分为两段, 每段区间上定义了不同的能量函数. 并给出了由LMI描述的新的时滞依赖鲁棒绝对稳定性判据.     

T-S 模糊时滞模型的时滞相关稳定性分析和镇定

研究一类用T—S模糊模型描述的非线性不确定时滞系统的时滞相关鲁棒镇定问题．基于线性矩阵不等式的可行解，首先给出利用T—S模糊模型描述的非线性时滞系统时滞相关稳定性准则；然后给出了经状态反馈鲁棒镇定设计的新方法．所设计的控制器能确保闭环系统渐近稳定．     

Delay-dependent criteria for robust stability of time-varying delay systems

This paper deals with the problem of delay-dependent robust stability for systems with time-varying structured uncertainties and time-varying delays. Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Since free weighting matrices are used to express this relationship and since appropriate ones are selected by means of linear matrix inequalities, the new criteria are less conservative than existing ones. Numerical examples suggest that the proposed criteria are effective and are an improvement over previous ones.     

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

     

不确定中立型系统鲁棒稳定及镇定的时滞相关准则

This paper concerns problem of the delay-dependent robust stability and stabilization for uncertain neutral systems. Some new delay-dependent stability criteria are derived by taking the relationship between the terms in the Leibniz-Newton formula into account. Free weighting matrices are given to express the relationship between the terms in the Leibniz-Newton formula and the new criteria are based on linear matrix inequalities such that the free weighting matrices can be easily obtained. Moreover, the stability criteria are also used to design the state-feedback controller. Numerical examples demonstrates that the proposed criteria are effective and are an improvement over the previous papers.     

针对准单边Lipschitz不确定非线性时滞系统的稳定性分析

研究了一类不确定非线性时滞系统的鲁棒稳定性. 准单边Lipschitz条件被介绍, 并被用于估计非线性向量函数在稳定性分析中的影响. 线性矩阵不等式形式的时滞无关/时滞相关稳定性判据被得到. 此外, 即使系统系数是不稳定的, 这些稳定性判据也是可利用的, 因为未必正定的准单边Lipschitz常数矩阵包含了很多非线性部分的有用信息. 数值实例证实了本文所获结果的有效性.     

Stabilization of a class of uncertain time-delay systems containing saturating actuators

The delay-dependent robust stabilization problem for a class of uncertain linear timedelay systems containing saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state. The delay is assumed to be constant bounded but unknown. New robust stability criteria and a sufficient condition for the existence of memoryless robust stabilizing control law are derived. The results depend on the size of the delay and are given in terms of several linear matrix inequalities (LMIs). A numerical example is presented to illustrate the obtained results.     

Delay-dependent robust H-infinity control for discrete-time uncertain systems with time-varying state delays

1 Introduction The analysis and synthesis of dynamic control systems with time delays is a subject of great practical and theo- retical importance, and has received considerable attention for decades (see [1,2] and references therein). Stability cri- teria can be classified roughly into two categories: delay- independent and delay-dependent [3]. Delay-independent criteria contains no information on the delay size, which, as might be expected, is generally conservative, especially when the dela…     

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.     

Delay-dependent robust stability analysis for interval linear time-variant systems with delays and application to delayed neural networks

Some delay-dependent robust asymptotical stability criteria for uncertain linear time-variant systems with multiple delays are established by means of parameterized first-order model transformation and the transformation of the interval uncertainty into the norm-bounded uncertainty. The stable regions with respect to the delay parameters are also formulated. Based on these results, we investigate the stability issue of a class of delayed neural networks that can be transformed into linear time-variant systems, and then several new global asymptotical stability criteria are exploited. Numerical examples are presented to illustrate the effectiveness of our results.     

Stability analysis for uncertain switched neutral systems with discrete time-varying delay: A delay-dependent method

This paper considers the robust stability of a class of switched neutral systems with discrete time-varying delay and time-varying structure. Sufficient conditions for exponential stability criteria are developed for arbitrary switching signal with average dwell time. The results are obtained based on Lyapunov’s stability analysis via Krasovsky–Lyapunov’s functionals and the related stability study is performed to obtain delay-dependent results. It is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are exponentially stabile. These conditions are delay-dependent and are given in the form of linear matrix inequalities (LMIs). Some examples are worked out to illustrate the effectiveness of the result.     

New delay-dependent stability criteria and stabilizing method for neutral systems

This note concerns delay-dependent robust stability criteria and a design method for stabilizing neutral systems with time-varying structured uncertainties. A new way of deriving such criteria is presented that combines the parameterized model transformation method with a method that takes the relationships between the terms in the Leibniz-Newton formula into account. The relationships are expressed as free weighting matrices obtained by solving linear matrix inequalities. Moreover, the stability criteria are also used to design a stabilizing state-feedback controller. Numerical examples illustrate the effectiveness of the method and the improvement over some existing methods.     

Delay-dependent robust stability criteria for singular time-delay systems by delay-partitioning approach

In this paper, the problem of delay-dependent robust stability for singular time-delay systems is investigated. The parametric uncertainties are assumed to be norm bounded. Based on the idea of delay partitioning, A new Lyapunov–Krasovskii functional is proposed to develop new delay-dependent criteria, that ensures the considered system to be regular, impulse free and stable in terms of linear matrix inequalities. Furthermore, the Wirtinger-based integral inequality approach has been employed to derive less conservative results. Finally, some numerical examples are provided to demonstrate the effectiveness of the obtained results and for comparison with previous works.     

区间时变细胞神经网络的全局鲁棒指数稳定性

研究了一类区间时变扰动、变时滞细胞神经网络的全局鲁棒指数稳定性问题．利用Leibniz-Newton公式对原系统进行模型变换,并分析了变换模型和原始模型的等价性．基于变换模型,运用线性矩阵不等式的方法,通过选择适当的Lyapunov-Krasovskii泛函,推导了该系统全局鲁棒指数稳定的时滞相关的充分条件．通过数值实例将所得结果与前人的结果相比较,表明了本文所提出的稳定判据具有更低的保守性．     

Stability of perturbed systems with time-varying delays

This paper gives easily verifiable sufficient conditions of robust asymptotic stability of linear time-delay systems subject to parametric unstructured or highly-structured perturbations. The criteria given in this paper are delay-independent or delay-dependent. The considered delay may be time-varying. An estimation of the transient behaviour of the studied systems is also provided (exponential rate of convergence).Scalar or vectorial inequalities involving Hurwitz matrices, matrix measures and norms constitute the mathematical foundations of the exposed results.