Delay‐dependent robust stability and stabilization for uncertain discrete singular systems with delays

The robust stability and robust stabilization for time‐delay discrete singular systems with parameter uncertainties is discussed. A delay‐dependent linear matrix inequality (LMI) condition for the time‐delay discrete systems to be nonsingular and stable is given. Based on this condition and the restricted system equivalent transformation, the delay‐dependent LMI condition is proposed for the time‐delay discrete singular systems to be admissible. With this condition, the problems of robust stability and robust stabilization are solved, and the delay‐dependent LMI conditions are obtained. Numerical examples illustrate the effectiveness of the method given in the paper. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

AN LMI APPROACH TO ROBUST STABILITY OF UNCERTAIN DISCRETE SINGULAR TIME‐DELAY SYSTEMS

The problem of robust stability analysis for uncertain discrete singular time‐delay systems is investigated in this paper. By decomposing the nominal system into slow and fast subsystems, a linear matrix inequality (LMI) condition is proposed for a discrete singular time‐delay system to be regular, causal and stable. Based on this, an LMI criterion is obtained for robust stability of an uncertain discrete singular time‐delay system. Two numerical examples are provided to demonstrate the feasibility of the proposed approach.     

不确定离散奇异时滞系统的鲁棒稳定性

针对一类具有区间时变时滞和线性分式参数不确定性的离散奇异系统, 研究鲁棒稳定性问题。基于Lyapunov稳定性理论, 应用线性矩阵不等式方法, 给出不确定离散奇异时滞系统的新的时滞相关型稳定性准则。所给准则相比于已有一些结果, 包含较少的矩阵变量, 且具有较小的保守性。数值实例表明所得结果的有效性。     

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.     

时滞依赖型中立系统的观测器设计与镇定

研究了一类时滞依赖型线性中立系统的观测器的设计与镇定问题,首先建立了一个时滞依赖型稳定性准则,基于LMI正定解的存在性,给出确保误差动力系统渐近稳定的充分条件及经状态反馈而达到镇定的设计方案.最后通过数值仿真来说明本文所得结论的正确性和有效性.     

不确定广义跳变时滞系统的鲁棒指数稳定性

讨论不确定广义跳变时滞系统的鲁棒指数稳定性问题. 利用线性矩阵不等式(LMI)技术给出一个时滞区间依赖条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 数值例子说明本文的结果改进了已有的结论.     

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.     

Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays

This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality （LMI） approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closed- loop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.     

Robust Stability and Stabilization Criteria for Discrete Singular Time‐Delay LPV Systems

This paper is concerned with establishing robust stability and stabilization criteria for discrete singular time‐delay linear parameter varying (LPV) systems. Firstly, a robust stability criterion is obtained for this class of systems by a delay‐partition approach, and thereby a less conservative sufficient condition which guarantees discrete singular time‐delay LPV systems to be admissible is given. Secondly, a class of state feedback controllers for stabilizing discrete singular time‐delay LPV systems is designed. Finally, compared with existing results, the numerical results of several examples illustrate the effectiveness of the approach proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

不确定线性多时变时滞系统的时滞相关鲁棒控制

提出一种积分不等式新方法，讨论不确定线性多时变时滞系统的鲁棒稳定性以及鲁棒稳定化问题，首先利用Park不等式建立了基于二次型项的积分不等式，利用这一不等式获得了系统基于LMI的时滞相关、时滞导数相关鲁棒稳定条件；然后利用这一条件给出了时滞状态反馈控制器的一种新的设计方法，数值例子说明了所得结论具有较小的保守性。     

Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays

This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality (LMI) approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closedloop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.     

分数阶系统线性矩阵不等式稳定判据的改进与鲁棒镇定: 0<α<1的情况

针对确定的分数阶系统,通过发掘其稳定区域与线性矩阵不等式(LMI)之间的联系,提出改进的LMI稳定判据.与已有结果相比,该判据形式简洁,求解变量少,且不含复矩阵变量,能够直接应用于控制器设计而不带来任何保守性,克服了原判据存在的主要缺点.然后基于该判据,进一步研究了当分数阶系统具有多胞型不确定时的鲁棒镇定控制器的设计方法.最后,仿真结果表明该方法的有效性.     

不确定时滞系统鲁棒镇定新方法

针对一类同时具有状态和控制滞后的不确定时滞系统,提出了一种新的时滞依赖型鲁棒镇定设计方法.通过引入一种新的线性状态变换,分离出时滞依赖因子,采用Lyapunov-Krasovskii泛函方法,导出了不确定时滞系统可鲁棒镇定的时滞依赖型的新判据,所得结论以线性矩阵不等式组的解的形式表示.仿真结果表明所得结论较之已有结果更为简单,具有更小保守性,且有更广泛的应用范围,不仅可以解决小时滞问题,也可用于解决大时滞问题.     

一类具有非线性不确定性的时滞系统鲁棒控制

研究一类具有非线性不确定参数以及状态滞后线性系统的时滞依赖鲁棒稳定性判据和鲁棒镇定问题。提出了新的鲁棒可镇定判据和相应的鲁棒无记忆状态反馈控制器设计方法,导出的时滞依赖结果以线性矩阵不等式的形式给出。     

参数摄动混杂离散系统的鲁棒稳定性

采用线性矩阵不等式(LMI)方法研究离散事件状态转移条件为状态依赖的参数摄动线性混杂离散系统的鲁棒稳定性问题, 提出此类系统全局鲁棒渐近稳定性判定定理, 基于分段Lyapunov函数给出了一般混杂离散系统在Lyapunov意义下局部稳定的判定定理, 该定理可将线性混杂离散系统的稳定性问题转化为LMI问题, 在此基础上提出了参数摄动线性混杂离散系统在Lyapunov意义下局部鲁棒稳定的充分条件.     

Stability and passivity analysis for Lur’e singular systems with Markovian switching

This paper is concerned with the stochastic stability and passivity analysis for a class of Lur’e singular systems with time-varying delay and Markovian switching. By using the free-weighting matrices approach, a delay-dependent stability criterion, which guarantees that the system is stochastically stable and robustly passive, is derived in terms of linear matrix inequality (LMI). Two numerical examples are provided to illustrate the effectiveness of the proposed method.     

不确定广义时滞系统的时滞依赖鲁棒H∞控制

讨论不确定广义时滞系统的时滞依赖鲁棒H∞控制问题. 基于线性矩阵不等式(LMI)方法, 设计状态反馈控制器使得对所有允许的不确定性, 所得的闭环系统均是正则、无脉冲、稳定且满足H∞范数有界约束. 所有的结论都是时滞依赖的且由不涉及系统矩阵分解的严格LMI表示. 数值例子表明所给的方法与已有的结论相比具有较小的保守性.     

ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME‐VARYING DELAYS

This paper deals with the problem of robust stability and robust stabilization for uncertain continuous singular systems with multiple time‐varying delays. The parametric uncertainty is assumed to be norm bounded. 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 purpose of the robust stabilization problem is to design a feedback control law such that the resulting closed‐loop system is robustly stable. This problem is solved via generalized quadratic stability approach. A strict linear matrix inequality (LMI) design approach is developed. Finally, a numerical example is provided to demonstrate the application of the proposed method.     

不确定广义时滞依赖鲁棒H∞控制

This paper discusses the problem of delay-dependent robust Ha control for uncertain singular systems with state delay. Based on linear matrix inequality (LMI) approach, we design a state feedback controller, which guarantees that, for all admissible uncertainties, the resultant closed-loop system is regular, impulse free, and stable with an H<,∞> norm bound constraint. All the obtained results are delay-dependent and formulated by strict LMI involving no decomposition of the system matrices. Numerical examples show that the proposed methods are less conservative than existing ones.