Decentralized Output Feedback Sliding Mode Control of Nonlinear Large-Scale Systems with Uncertainties

In this paper, a class of nonlinear large-scale interconnected systems with mismatched uncertainties is considered. Based on sliding mode control ideas, a kind of decentralized robust control scheme using only output information is presented to stabilize the system. The approach allows more general uncertain interconnections than all of the associated existing work and better robustness is achieved. Compared with existing decentralized output feedback schemes, it is unnecessary to solve Lyapunov equations and the so-called strict structural condition is avoided. Also, it is not necessary that the nominal subsystem is output feedback stabilizable. Finally, a simulation example is presented to illustrate the effectiveness of the results.     

Stochastic Output Feedback of Uncertain Time-Delay Systems with Saturating Actuators

This paper deals with the class of uncertain continuous-time linear systems with Markovian jumps, time delay, and saturating actuators. Under norm-bounded uncertainties and based on the Lyapunov method, sufficient conditions on stochastic stability and stochastic stabilizability are developed. A design algorithm for a stabilizing observer-based robust output feedback controller is proposed in terms of the solutions of linear matrix inequalities.     

具有分离变量的非线性随机时滞相关系统的鲁棒稳定

本文研究一类具有分离变量的非线性随机不确定系统的稳定性问题。采用线性矩阵不等式（LMI）和Lyapunov—Krasovskii泛函的方法，获得了局部指数稳定性的时滞盯关性判据。仿真结果证明了结论的可行性和优越性。     

具有未知增长率的非线性系统的一般适应控制

阐明对于一类不确定系统在适当的条件下如何设计适应输出反馈控制器.这个不确定性来源于系统的未知参数.设计了一般输出反馈控制器结合Barbalat's引理从而证明系统的所有状态全局稳定.     

基于输出反馈的一类大型互联非线性系统的鲁棒全局指数稳定

研究基于输出反馈的一类新的大型互联非线性不确定系统的鲁棒全局指数稳定问题,通过构造每个子系统收敛的状态观测器,并对观测器的状态作线性变换,得到鲁棒分散输出反馈控制器.当该反馈控制律作用于该系统时,闭环系统是全局指数稳定的.     

Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties

In this paper, the problem of the robust stabilization for a class of uncertain linear systems with multiple time-varying delays is investigated. The uncertainty is nonlinear time-varying and does not require a matching condition. A memoryless state-feedback controller for the robust stabilization of the system is proposed. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, two sufficient conditions for the stability are derived. Two numerical examples are given to illustrate the proposed method.     

Robust Guaranteed Cost Decentralized Stabilization for Uncertain Discrete Large-Scale Systems with Delays via State Feedback and Output Feedback

The problem of robust guaranteed cost decentralized stabilization for uncertain discrete large-scale systems with delays is investigated in this paper. Sufficient conditions for the existence of the robust guaranteed cost decentralized controllers via memoryless state feedback and static output feedback are expressed as BMIs. Furthermore, alternate iterative algorithms are proposed to solve the feasible problems with BMI constrains. Numerical examples are given to illustrate effectiveness of the proposed methods.     

On State Feedback Stabilization of Singular Systems with Random Abrupt Changes

This paper deals with the class of continuous-time singular linear systems with random abrupt changes. The state feedback stabilization and its robustness for this class of systems with norm-bounded uncertainties are tackled. Sufficient conditions for designing either a stabilizing controller or a robust stabilizing controller are developed in the LMI setting. The developed sufficient conditions are used to synthesize the state feedback controller that guarantees that either the nominal system or the uncertain system is piecewise regular, impulse free and stochastically stable or robust stochastically stable. The research of this author was supported by NSERC, Grant RGPIN36444-02.     

Necessary and Sufficient Condition for Robust Stability and Stabilizability of Continuous-Time Linear Systems with Markovian Jumps

In this paper, we investigate the quadratic stability and quadratic stabilizability of the class of continuous-time linear systems with Markovian jumps and norm-bound uncertainties in the parameters. Under some appropriate assumptions, a necessary and sufficient condition is established for mean-square quadratic stability and mean-square quadratic stabilizability of this class of systems. The quadratic guaranteed cost control problem is also addressed via a LMI optimization problem.     

Stabilization of Passive Nonlinear Stochastic Differential Systems by Bounded Feedback

Abstract

The purpose of this paper is to give a systematic method for global asymptotic stabilization in probability of nonlinear control stochastic differential systems the unforced dynamics of which are Lyapunov stable in probability. The approach developed in this paper is based on the concept of passivity for nonaffine stochastic differential systems together with the theory of Lyapunov stability in probability for stochastic differential equations. In particular, we prove that, as in the case of affine in the control stochastic differential systems, a nonlinear stochastic differential system is asymptotically stabilizable in probability provided its unforced dynamics are Lyapunov stable in probability and some rank conditions involving the affine part of the system coefficients are satisfied. Furthermore, for such systems, we show how a stabilizing smooth state feedback law can be designed explicitly. As an application of our analysis, we construct a dynamic state feedback compensator for a class of nonaffine stochastic differential systems.