参数不确定广义大系统的分散鲁棒镇定控制

应用线性矩阵不等式(LMI)方法研究了参数不确定广义大系统的分散鲁棒镇定控制问题，系统中不确定项具有数值界，可不满足匹配条件．基干不确定项的表达形式，给出了存在分散鲁棒控制器的LMI条件．仿真例子表明，LMI方法求解简单、便干应用。     

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.     

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.     

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 stabilization for generalized state-space systems with uncertainty

This paper is concerned with the problem of robust stabilization for generalized state-space systems with parameter uncertainty. The parameter uncertainty under consideration is time-invariant and unknown, but is norm-bounded. The problem we address is to design a state feedback controller such that the resulting closed-loop system is regular, impulsefree and stable for all admissible uncertainties. Via the notion of 'stabilizability and impulse eliminatibility' the robust stabilization problem is solved. Necessary and sufficient conditions for stabilizability and impulse eliminatibility are derived. When these conditions are satisfied, the desired stabilization state feedback controller can be constructed through finding parameters satisfying a certain matrix equation. Finally, an illustrative example is given to show the feasibility of the proposed technique.     

Robust stabilization for systems with rank-one uncertainty structure

This paper solves a class of robust control problems, with output feedback, for systems with mixed parametric uncertainty and unmodeled dynamics. This class of problems is characterized by a special rank-one assumption on the transfer matrix of the nominal plant. Under this assumption, the robust stabilization problem is reduced to a convex feasibility problem involving linear matrix inequalities. The data necessary to assemble these inequalities can be readily obtained from a state-space model of the nominal plant.     

不确定广义系统的时滞依赖鲁棒镇定

研究不确定广义系统的时滞依赖鲁棒镇定问题。利用Lyapunov泛函方法,得到一个线性矩阵不等式(LMIs)形式的时滞依赖稳定与镇定判据。新方法考虑一些以前方法中通常忽略的有用的项,引入一些自由权重矩阵,估计Lyapunov泛函导数的上界;再用凸优化算法,进一步给出状态反馈控制器的设计方法。最后通过两个仿真示例表明了新方法的有效性。     

Robust stability and stabilization of discrete singular systems: an equivalent characterization

This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.     

Robust stabilization for uncertain discrete singular systems with state delay

The robust stabilization problem for uncertain discrete singular time‐delay systems is addressed in this paper. In terms of strict linear matrix inequality and a finite sum inequality, a delay‐dependent criterion for the nominal systems to be admissible is obtained. Based on the criterion, a state feedback controller, which guarantees that, for all admissible uncertainties, the resulting closed‐loop system is regular, causal and stable, is constructed. An explicit expression for the desired controller is also given. The obtained results include both delay‐independent and delay‐dependent cases. Some numerical examples are introduced to show the effectiveness of the given results. Copyright © 2008 John Wiley & Sons, Ltd.     

参数和时延不确定性离散时间系统的 H∞鲁棒控制

针对含有参数和时延不确定性线性离散时间系统的鲁棒控制问题，构造改进的Lyapunov函数，并采用LMI与H∞鲁棒控制相结合的方法，使得系统在不含外界未知扰动时，只得满足一个矩阵不等式，便可通过状态的静态反馈控制使闭环系统达到二次稳定；而在系统含有外界未知扰动时，结合基于离散时间系统的无源性控制方法，同样只得满足一个矩阵不等式，便可通过状态的静态反馈控制使得闭环系统达到理想的干扰抑制作用。     

基于观测器的不确定广义时滞系统鲁棒预测控制

针对一类不确定广义时滞系统,讨论了其基于观测器的鲁棒预测控制问题,给出了系统观测器型预测控制器的设计方法.通过构造带有误差项的Lyapunov函数,应用线性矩阵不等式,将无穷时域二次性能指标"min-max"优化问题转化为凸优化问题,得到了鲁棒预测控制器存在的充分条件和显式表达式.证明了优化问题在初始时刻的可行解能保证广义闭环系统渐近稳定且正则无脉冲.仿真实例验证了所提出方法的有效性.     

具Frobenius有界不确定性广义系统的鲁棒稳定性

研究了具Frobenius有界不确定性广义系统的稳定与鲁棒镇定问题. 通过对代数Riccati不等式或代数Riccati方程的求解, 获得了不确定广义系统广义二次稳定的充要条件, 使得对所有容许的不确定参数, 系统是稳定, 正则和无脉冲. 而且, 根据一类矩阵方程, 构造了使不确定广义系统鲁棒镇定的状态反馈控制器的设计方法. 实例说明了上述方法的有效性.     

Robust V stabilization of singular systems with polytopic uncertainties

The robust D stabilization problem is considered for singular systems with polytopic uncertainties in this paper. Both the derivative matrix E and the state matrix A are with uncertainties, which were not considered before. First, with the introduction of some free matrices, a necessary and sufficient condition for the singular system to be D stable is proposed, based on which, the robust D stable problem is solved, and a sufficient condition for the closed system to be robust D stabilizable is obtained. The desired state feedback controller is given in an explicit expression. Numerical examples show the efficiency of the proposed approach.     

Robust D stabilization of singular systems with polytopic uncertainties

The robust D stabilization problem is considered for singular systems with polytopic uncertainties in this paper. Both the derivative matrix E and the state matrix A are with uncertainties, which were not considered before. First, with the introduction of some free matrices, a necessary and sufficient condition for the singular system to be D stable is proposed, based on which, the robust D stable problem is solved, and a sufficient condition for the closed system to be robust D stabilizable is obtained. The desired state feedback controller is given in an explicit expression. Numerical examples show the efficiency of the proposed approach.     

一类不确定离散奇异系统的鲁棒稳定化

讨论了离散奇异系统矩阵E中含时不变参数不确定的鲁棒状态反馈稳定化问题.首先,在一系列等价变换下,阐述了其和一个不确定正常线性离散系统的鲁棒状态反馈稳定化问题的等价关系;然后,利用线性矩阵不等式(LMI)方法,给出了鲁棒状态反馈稳定化控制器存在的一个充分必要条件,控制器的设计方法及控制器的一个解;最后,通过一个数值算例验证了本设计方法的有效性.     

参数不确定广义大系统的保性能分散控制

对一类范数有界时不变参数不确定的连续广义大系统和一个二次型性能指标,研究了其保性能分散控制问题.目的是设计一状态反馈分散控制器,使得对所有容许的不确定性,闭环系统不仅是鲁棒稳定的,而且性能指标有一上界.应用线性矩阵不等式方法,给出了一个用线性矩阵不等式表达的保性能分散控制器存在的充分条件;在此条件可解时,给出了保性能分散控制律的表达式.最后,举例说明了该方法的应用.     

Robust stabilization of linear systems with norm-bounded time-varying uncertainty

In this paper, robust stabilization of a class of linear systems with norm-bounded time-varying uncertainties is considered. It is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a (parameter-dependent) Riccati equation. Also, a construction for the stabilizing feedback law is given in terms of the solution to the Riccati equation.     

多时滞奇异系统鲁棒稳定性分析

讨论了多时滞奇异系统的鲁棒稳定性问题．通过构造一种新的Lyapunov—Krasovskii泛函（LKF）,结合离散化LKF理论,给出了多时滞奇异系统正则、脉冲自由和渐近稳定的充分条件,并将该结论推广到含有范数有界不确定性的多时滞奇异系统．数值算例验证了该方法的有效性和可行性．     

具有状态时滞的切换随机系统的指数稳定条件

考虑由具有状态时滞的线性It(o)随机子系统构成的切换系统,基于多Lyapunov泛函方法研究切换与时滞对于稳定性的共同影响,并以此建立均方指数稳定条件.在均方意义下噪声对于稳定性的影响基本是负面的,因此构造一类形式较为一般的Lyapunov泛函并运用噪声的统计特性于其解析过程中,以减少噪声所引起的保守性.最后,通过一个仿真算例描述切换与时滞的相互制约关系表明了所提出方法的有效性.     

Robust stabilization of singular markovian jump systems with uncertain switching

This paper focuses on the robust stabilization problem for a class of singular Markovian jump systems with uncertain switching probabilities. Based on a slack matrix method on transition probabilities, a new criterion for quadratically stochastic admissibility of such an uncertain system is established. Then, two new sufficient conditions for the existence of mode-dependent controller are given as linear matrix inequalities. Especially, a more practical controller named as mode-independent controller is derived by a mode-dependent Lyapunov function. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.