An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality (LMI). Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.     

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.     

Delay-dependent robust observer-based control for discrete-time uncertain singular systems with interval time-varying state delay

The problem of observer-based robust control design is studied for discrete-time singular systems with norm-bounded uncertainties and a time-varying delay. More precisely, a delay-dependent criterion is established that guarantees the admissibility of the considered systems, without resorting to its decomposition. Based on the proposed criterion and without the assumption that the considered systems are admissible, robust observer-based controllers are designed for discrete-time singular time-delay systems such that the closed-loop systems have the characteristics of regularity, causality and asymptotic stability. Seeking computational convenience, all the developed results are cast in the format of strict linear matrix inequalities (LMIs). Finally, some numerical examples are presented to show the feasibility of the proposed approach.     

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…     

一类不确定切换奇异时滞系统的时滞依赖鲁棒镇定

针对一类不确定切换奇异时滞系统,对其鲁棒镇定问题进行了研究.首先利用多李亚普诺夫泛函方法和线性矩阵不等式工具,通过引入适当的自由权矩阵,在适当的切换律下,给出了基于严格线性矩阵不等式表示的标称自治切换奇异系统正则、无脉冲且渐近稳定的时滞依赖条件;然后基于此条件,通过设计相应的状态反馈子控制器,得到了保证闭环系统对所有允许的不确定性是正则、无脉冲且渐近稳定的时滞依赖条件,同时给出了子控制器的显示表达式.数值算例表明该方法的有效性.     

不确定奇异时滞系统的时滞相关型鲁棒H∞弹性控制

研究了含范数有界参数不确定性的奇异时滞系统的时滞相关型鲁棒H_∞弹性控制问题.文中所考虑的控制器增益摄动包括加性摄动和乘性摄动两种形式.在标称奇异时滞系统的时滞相关型稳定性判据的基础上,引入了一个新的时滞相关型有界实引理(BRL),进而给出了时滞相关型鲁棒H_∞弹性控制器存在的充分性条件,并利用LMIs和锥补线性化算法给出了控制器的表达式.从数值算例可以看出,所给出的设计算法是有效的.     

一类新的Takagi-Sugeno模糊时滞系统的稳定性准则

本文提出一种新的时滞划分方法—变时滞划分法,以解决连续延时Takagi-Sugeno模糊系统的稳定性和镇定性问题.不同于已有的文献,用可变参数将时变时滞区间[0,d(t)]划分为若干个可变子区间,并得出模糊时滞系统的新的时滞相关稳定性准则.本文提出的新方法能充分利用时滞子区间的内部信息,因此新的时滞相关稳定性准则比以往结果具有更小的保守性.基于Lyapunov稳定性理论,以线性矩阵不等式形式给出T--S模糊系统的新的时滞相关稳定性准则,并将稳定性和镇定性研究结果扩展到具有不确定参数的T--S模糊系统.仿真实例证明了本文方法降低保守性的有效性.     

不确定奇异时滞系统的时滞相关型鲁棒∞弹性控制

讨论了不确定奇异时滞系统的时滞相关型鲁棒弹性控制器设计问题.在一个关于标称奇异时滞系统的新的时滞相关型稳定性判据的基础上给出了一种新的有界实引理(BRL:bounded real lemma);基于此给出了时滞相关型鲁棒弹性控制器存在的充分性条件,最后通过数值算例说明本文结果的有效性.     

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.     

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

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach.     

含离散与分布时滞的不确定中立型系统鲁棒稳定性新判据

基于离散时滞分解思想,通过构造一种新的Lyapunov-Krasovskii泛函并结合Jensen不等式技巧,建立了线性矩阵不等式(LMI)形式的时滞相关鲁棒稳定性新判据.该方法允许中立时滞项的系数矩阵存在时变不确定性,增强了系统的鲁棒性能.同时针对分布时滞项难于处理的问题,构造了其分解计算泛函.数值算例表明所得结论的有效性和更低的保守性.     

Delay-dependent H-infinity control for continuous time-delay systems via state feedback

The delay-dependent H-infinity analysis and H-infinity control problems for continuous time-delay systems are studied. By introducing an equality with some free weighting matrices, an improved criterion of delay-dependent stability with H-infinity performance for such systems is presented, and a criterion of existence and some design methods of delay-dependent H-infinity controller for such systems are proposed in term of a set of matrix inequalities, which is solved efficiently by an iterative algorithm. Further, the corresponding results for the delay-dependent robust H-infinity analysis and robust H-infinity control problems for continuous time-delay uncertain systems are given. Finally, two numerical examples are given to illustrate the efficiency of the proposed method by comparing with the other existing results.     

不确定奇异时滞系统时滞依赖鲁棒镇定

This paper considers the problem of delay-dependent robust stabilization for uncertain singular delay systems.In terms of linear matrix inequality (LMI) approach,a delay-dependent stability criterion is given to ensure that the nominal system is regular,impulse free,and stable.Based on the criterion,the problem is solved via state feedback controller,which guarantees that the resultant closed-loop system is regular,impulse free,and stable for all admissible uncertainties.An explicit expression for the desired controller is also given.Some numerical examples are provided to illustrate the validity of the proposed methods.     

Delay dependent robust stability of singular systems with additive time-varying delays

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.     

具有多输入时滞的不确定广义系统的时滞相关鲁棒镇定

研究具有多输入时滞及参数不确定性的广义系统的时滞相关鲁棒镇定问题. 首先利用LMI给出相应的标称系统的时滞相关镇定准则. 然后, 基于这个准则, 设计状态反馈控制器, 使得对任何允许的不确定参数相应的闭环系统是正则, 稳定, 无脉冲的. 最后的数值算例表明所提方法是有效的.     

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.     

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.     

含区间时变时滞的线性不确定系统非脆弱鲁棒控制

针对一类时滞是时变的且属于一个已知区间的线性系统,利用Lyapunov-Krasovskii泛函方法,结合积分不等式方法,以线性矩阵不等式的形式,给出了区间时滞线性系统的时滞相关鲁棒稳定性准则,并设计了非脆弱鲁棒控制器。数值算例表明,所得结论是有效的,具有更低的保守性。     

Delay-dependent approach to robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties

A delay-dependent approach to robust H _∞ filtering is proposed for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties. The delays are interval time-varying delays and uncertainties are a convex compact set of polytopic types. The aim of the designed filter is to guarantee regular, causal, asymptotic stability with H _∞ norm bound of filtering error singular systems. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded lemma (BL) for singular systems with interval time-varying delays is proposed. Based on the result, the existence condition of the robust H _∞ filter and the filter design method are presented in terms of linear matrix inequality (LMI). Finally, two examples are also given to illustrate the effectiveness of the proposed methodology.