Stability And Decentralized Control For The Singular Large-Scale Systems

The asymptotic stability and stabilization problem is one of the fundamental problems in the theory of singular large-scale system. The study of them is much more complicated than that of state-space systems because the singular large-scale system requires considering not only stability, but also regularity and causality (for discrete singular systems) or impulse immunity (for continuous singular systems) . The large-scale systems are difficult to control due to large in scale, numerous factors and lack of centralized computing capability, etc. Some of the difficulties associated with a centralized control scheme can be alleviated via a decentralized control structure in which information transfer between subsystems is unavoidable. Therefore, decentralized control is considered as an effective method to deal with large-scale systems.In the light of the recent work on singular large-scale systems models, especially in linear singular large-scale systems models, the dissertation provides a systematic study on the asymptotic stability, decentralized stabilization and guaranteed cost control of linear singular large-scale systems models and singular large-scale systems with parameter uncertainty. The main results obtained in this dissertation are as follows:i) The problems of asymptotic stability and unsteadiness of continuous singular linear large-scale system and continuous singular non-linear large-scale system are investigated by means of Lyapunov equation and Lyapunov function under the conditions that all their isolated subsystems are of regularity and impulse immunity. The theorems of asymptotic stability and unsteadiness of continuous singular large-scale systems are presented. The interconnecting parameter regions of asymptotic stability and unsteadiness for them are obtained.ii) The problems of asymptotic stability and unsteadiness of discrete singular linear large-scale system and discrete singular non-linear large-scale system are investigated by means of Lyapunov equation and Lyapunov function under the conditions that all their isolated subsystems are of regularity and causality. The theorems of discrete singular large-scale systems asymptotic stability and unsteady are presented. The interconnecting parameter regions of asymptotic stability and unsteadiness for them are obtained.iii) The Lyapunov s method and Lyapunov equation are employed to study the asymptotic stability and stabilization problem on discrete (continuous) singular large scalesystems under the conditions that all their isolated subsystems are regularity and impulse immunity (for continuous singular systems) or causality (for discrete singular systems) and R-controllable. The theorem of asymptotic stability is obtained. The controller is designed for the stabilization of singular large-scale systems. The utilized method is simple, intuitional and easily understood. An example shows that the theorem is feasible.iv) This paper addresses the problems of robust stable and robust stabilization for uncertain continuous-time singular large-scale systems with parameter uncertainties via linear matrix inequality (LMI) method. The parameter uncertainties are assumed to be time invariant, but norm-bounded. The purpose of the underlying robust stabilization problem discussed in this paper is to design state feedback controllers so that, for all admissible uncertainties, the closed-loop system is of regularity and impulse immunity. In terms of strict LMIs, sufficient conditions for the solvability of above problems are presented, and the parameterizations of the desired state feedback controllers are also given. A numerical example is given to demonstrate the applications of the proposed design.v) This paper addresses the problems of robust stable and robust stabilization for uncertain discrete-time singular large-scale systems with parameter uncertainties by LMI method. The parameter uncertainties are assumed to be time invariant, but norm-bounded. The purpose of the underlying robust stabilization problem discussed in this paper is to design state fee...