The Stability Analysis And Robust Control For Nonlinear Large-scale Interconnected System

The study of nonlinear interconnected large-scale systems in recent years has been widely attention at home and abroad. It is not only prevalent in the social system, administrative system, complex social and economic systems, in various engineering also has been widely used in the system. Such as fleet communications system, power systems, environmental pollution problems, military escort CI system question, the economic dynamic input-output system and so on. The decentralized control for its reliability, economy, practicality and flexibility to achieve an important branch of the large system theory, therefore, for the decentralized control of nonlinear interconnected large-scale systems research has a very important theoretical and practical value.Through study of the structure of the systems, construct a suitable LyapunovKrasovskii function, exploiting the integral inequalities, Lyapunov stability theory, linear matrix inequality(LMI) and other methods to study the decentralized robust stabilization and the problem of H_∞control for the nonlinear large-scale connected systems. The main contents are as follows:Firstly, Nonlinear time varying delay interconnected systems with nonlinear isolated nominal subsystems and nonlinear time delay interconnections are considered in this paper, where the nonlinear state vectors involve time delay. The new structure is presented via Taylor expansion. Based on which, by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralized memory static output derivative feedback controllers are designed, which is dependent of time delay, to stabilize the interconnected systems uniformly asymptotically.Secondly, the problems of robust H_∞hybrid feedback control for a class of nonlinear time delay singular large scale systems with perturbation is investigated. Based on the bounded real lemma, LMI method, construct a new Lyapunov function, the corresponding linear matrix inequalities(LMI) gives a sufficient condition that stabilize the closed-loop system asymptotically stable and to ensure that the closed-loop system to meet certain performance and given the method of design the H_∞controller, finally the simulation results show the effectiveness of this method.Finally, In this paper, the problems of decentralized memory proportionalplus-derivative state feedback control for a class of singular time-delay interconnected systems with similar structure is investigated, the new similar structure is presented via memory proportional-plus-derivative state feedback, by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralized memory proportional-plus-derivative state feedback controller with similar structure is designed, witch is dependent of time delays, to stabilize the interconnected systems uniformly asymptotically, and estimated the stable area of the systems.