On Problems Of Stability For Two Kinds Of Composited Systems

The most important feature of automatic control systems is stability. It means that the system can properly maintain the scheduled working state and tolerant the effects of various adverse factors. Stability control system is essen-tially its own property issues. With the development of science and technology, the structure of control systems become increasingly complex. Classical control theory is unfit for the analysis of modern control systems. After 60's, the rapid development of the theory of state space analysis, which led to Lyapunov's theory to be seriously and achieved many fruitful results. Now we use this method to analyze the stability of the following two types complex systems.In the first chapter briefly describes the background of the composite systems and the singular system, in addition, the present study situation and the existing problems.In the second chapter the problem of stability of composite nonlinear systems with uncertainty is discussed. A new stability criterion for the systems is deduced by using differential equation theory, matrix similar transformation and matrix exponential properties. The problem of stability of composite nonlinear systems can be translated into that of a linear system, hence, a new sufficient condition for testing stability of original systems is proposed. In this paper, the uncertainty and nonlinearity are estimated by a vector. It's not necessary to require them having norm bounder or other strict matching conditions, and it does not require the state matrixes of subsystems is Hurwitz matrix. Our method reduces the conversation of previous references. Finally, one demonstrative example is used to show the availability and the effectiveness of the proposed approach.The nonlinear interconnected systems are widely used in power systems, communication systems ecosystems and so on. In the third chapter the stability of this kind of systems with uncertainty and without uncertainty are respectively discussed. By using Lyapunov functions, Schur complement principle and the properties of M matrix under the conditions that uncertainty and nonlinearity having norm bounder without other strict matching conditions. new criteria for the asymptotic stability of the nonlinear large-scale systems are proposed in the form of N order matrix and LMI.The chapter four discusses the stability of the singular large-scale systems. The sufficient conditions for singular composite systems is developed by using Lyapunov functions and the methods of LMI. The second part of the chapter discusses the robust H∞decentralized control for nonlinear singular compos-ite systems with time-delay. The problems of stability and stabilization for singular system were discussed frequently in the former references, this arti-cle has been made the corresponding expansion on the basis of previous liter-ature, also, the H∞performence of the systems is considered. Keywords nonlinear composite systems; differential equation; linear matrix inequalities; singular systems...