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.     

基于LMI的分布时滞系统输出动态反馈镇定

研究分布时滞系统的输出动态反馈镇定问题. 基于闭环系统的中立型变换及相应Lyapunov-Krasovskii泛函的构造与解析技巧, 建立了与时滞相关的控制器存在性判据. 在此基础上通过控制器参数化设计方法, 将控制器参数的求解归结为线性矩阵不等式解的形式. 仿真算例验证了方法的有效性     

含未知输入的时滞系统的函数观测器及输出反馈镇定

考虑了含未知输入的时滞系统的线性函数观测器设计.在一个不失一般性的秩条件假定下,以线性矩阵不等式(LMI)的形式给出了观测器存在的时滞无关型及时滞相关型判据,进而得到函数观测器改进的设计方法.此外,还讨论了降维状态观测器的设计,给出了基于观测器的反馈镇定控制器,实现了闭环的特征根分离及内稳定.具体算例说明了本文方法的有效性.     

Stability and stabilization of continuous-time singular hybrid systems

In this paper, the problems of stability and state feedback stabilization for a class of continuous-time singular hybrid systems are investigated. A new sufficient and necessary condition for a continuous-time singular hybrid system to be regular, impulse-free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Moreover, a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.     

离散广义区间系统的保成本控制

分析了离散广义区间系统的保成本控制问题.当系统参数在某一确定区间变化时,控制器能保证闭环系统稳定和一定的线性二次型性能指标上界.基于Lyapunov稳定性理论,该控制器的设计可转化为线性矩阵不等式的可解性问题.数值仿真也验证了所给方法的有效性.     

Control for discrete singular hybrid systems

The problems of stability, state feedback control and static output feedback control for a class of discrete-time singular hybrid systems are investigated in this paper. A new sufficient and necessary condition for a class of discrete-time singular hybrid systems to be regular, causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict LMIs, respectively. Finally, two illustrative examples are provided to demonstrate the applicability of the proposed approach.     

Delay-dependent stability analysis for Markovian jump systems with interval time-varying-delays

This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities (LMIs), less conservative delay-range-dependent stability conditions for Markovian jump systems are proposed by constructing a different Lyapunov-Krasovskii function. The resulting criteria have advantages over some previous ones in that they involve fewer matrix variables but have less conservatism. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper.     

Dynamic output‐feedback control for continuous‐time singular Markovian jump systems

This paper considers a dynamic output‐feedback control for continuous‐time singular Markovian jump systems, whereas the existing research studies in literature focused on state‐feedback or static output‐feedback control. While they have only provided the sufficient conditions, this paper successfully obtains the necessary and sufficient condition for the existence of the dynamic output‐feedback control. Furthermore, this condition is expressed with linear matrix inequalities by the so‐called replacement technique. Two numerical examples show the validity of the resulting control.     

Descriptor discrete-time systems with random abrupt changes: stability and stabilisation

This paper deals with the class of linear discrete-time systems with random abrupt changes also known as class of Markovian jump singular systems. The problems of stochastic stability and the stochastic stabilisation (using state-feedback control and static output feedback control) are tackled. Conditions in the LMI setting to design the appropriate gains of the controllers are developed. It is shown that all the addressed problems can be solved if the corresponding developed linear matrix inequalities (LMIs) are feasible. Numerical examples are employed to show the usefulness of the proposed results.     

Output feedback decentralized stabilization: ILMI approach

In this paper, the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach. A necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time-invariant large-scale systems. It is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality. The extension of the result to control is studied. An iterative LMI algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain. Examples show the effectiveness of the algorithm.     

Less conservative robust stability criteria for uncertain discrete stochastic singular systems with time-varying delay

The problem of robust stabilisation for uncertain discrete singular systems with time-varying delay is discussed in this article. First, a new delay-distribution-dependent Lyapunov function is established. Then, sufficient conditions are proposed for guaranteeing that the uncertain discrete singular system with time-varying delay has the properties of regularity, causality and stability. Finally, a suitable robust state feedback controller is designed by linear matrix inequality. Numerical examples illustrate that the results derived from the proposed method are less conservative than the existing ones.     

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.     

滞后广义系统的状态反馈H∞控制

研究了一类状态方程和输出方程均带有时滞的滞后广义系统的H_∞控制问题.利用线性矩阵不等式,首先给出滞后广义系统零解渐近稳定且具有H_∞范数约束的充分条件,进而分别设计无记忆和有记忆状态反馈控制律,保证闭环系统具有上述性能,同时基于线性矩阵不等式的解得到了相应控制器构造方法.最后给出一个数值算例说明文中结论的有效性.     

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.     

不确定脉冲系统的动态输出反馈H∞控制

研究了不确定脉冲系统动态输出反馈H_∞控制问题. 考虑了两类脉冲形式: 一类脉冲是扰动型的, 一类脉冲是稳定型的. 对每类脉冲系统, 给出了鲁棒稳定性和具有有限L2增益的充分条件. 并在此基础上, 基于线性矩阵不等式, 得到了H_∞动态输出反馈控制器存在的充分条件. 最后, 数值例子说明了本文结果的有效性.     

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.     

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality(LMI). Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.     

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     

模糊不确定时滞系统的静态输出的反馈镇定:迭代线性矩阵不等式方法

对一类不确定非线性时滞系统利用模糊T＿S模型进行建模,研究了静态输出反馈镇定问题.用矩阵不等式的形式给出了模糊T＿S不确定时滞系统可通过静态输出反馈镇定的充分条件.并将矩阵不等式的条件转化为迭代线性矩阵不等式(ILMI),并给出相应的算法.     

Admissibility and static output‐feedback stabilization of singular Markovian jump systems with defective statistics of modes transitions

This paper presents a necessary and sufficient condition for discrete‐time singular Markovian jump linear systems with defective statistics of modes transitions to be regular, causal, and stochastically stable. The static output‐feedback stabilization problem for discrete‐time singular Markovian jump linear system with defective statistics of modes transitions is studied. Furthermore, the defective statistics about modes transitions are studied by considering the uncertain transition probabilities and partially unknown transition probabilities situations account in a composite way. The closed‐loop system is represented in an augmented form, in which input and gain‐output matrices are separated. By virtue of the system augmentation, a sufficient condition for the existence of desired controllers is established. An extension to mode‐independent static output‐feed stabilization is provided as well. Copyright © 2013 John Wiley & Sons, Ltd.