Uncertain Systems Robust H_ ¡Þ Control

The robust H∞control problems are studied based on linear matrix inequality(LMI) approach in this dissertation. The main results can be listed as follows:In the first part, we focus on the problem of the robust H∞control design for discrete-time linear system with the uncertainties which are modeled as a polytopic type with linear fractional uncertainties in the vertices. The problem is solved by the linear matrix inequalities(LMIS ). With the introducing of a general matrix variable which can decouple the Lyapunov matrix and the system matrices, we can get a new LMI characterization of the H performance for the discrete-time systems. This feature enables one to get a sufficient conditions for the discrete-time system by using parameter-dependent Lyapunov function with less conserva-tiveness.In the second part, we study the problem of the robust H∞ control design for linear uncertain system with time-delay in which the uncertainties are modeled as a linear fractional form. A sufficient delay-dependent condition is given in the form of linear matrix inequalities. The design of state feedback controller is developed based on the linear matrix inequalities approach.In the third part, we propose a LMI design methodology for a class of discrete-time uncertain time-delay system with guaranteed H∞ performance based on the result of the first part. The approach of robust H∞ controller design isgiven.