Study On Guaranteed Cost Control For Uncertain Systems System

With the development of the society, there are all kinds of system models, for example, generalized system and neutral system and so on. The generalized system is often used in economic systems and electronic network. Generalized systems, which also aee called coupled systems, differential algebraic systems or implicit systems, as we all know the Hopfield neural network models, and some sorts of power systems. In recent years, there are also many people studied the bility of various of neutral system, thus the study of neutral delay systems has important practical significance and far-reaching influence. For actual system, however, only to guarantee the stability is not enough, and we ensure that the system response could meet certain performance indicators, so we put forward the problem of guaranteed cost control research. In the process of all kinds of actual control, this method is widely used, and it has important theoretical and practical value, and studied by many scholars. In this paper, we study several typestas of the uncertainty system design method of guaranteed cost controller.1. By studying the parameters of the guaranteed cost control problem of uncertain linear generalized systems, and design a state feedback controller with memory, using the linear matrix inequality(LMI) will be the guaranteed cost control of linear generalized system research for promotion, and decide whether a given system sufficient conditions for the existence of state feedback guaranteed cost control law and expression form. Finally, by two numerical simulation we prove the feasibility and effectiveness of the method.2. For a class of uncertain parameters and nonlinear disturbances of the guaranteed cost control problem of neutral delay system, the designed controller is allowed by the parameters uncertainty and time-delay, which is based on linear matrix inequality(LMI) and Lyapunov stability theory, and through getting the delay-dependent stability criterion and the design method of guaranteed cost controller, getting the least upper bound of performance index. Finally, numerical examples will prove that the designed controller is effective and feasible.3. we study the guaranteed cost control problem of nonlinear singular systems with time-delays, through the study with delay and related nonlinear disturbances of guaranteed cost control problem of uncertain generalized systems, and next we design a state feedback controller with memory. Its disturbance meets the demands of Lipschitz conditions, and bases on the Lyapunov stability theory and the linear matrix inequality(LMI) approach. Finally, the feasibility of this method is presented by some numerical examples.