H_∞Control For A Class Of Nonlinear Singular Systems With Delays

The delay phenomenon often occurs in physics, biology, and various practical problems, causing many scholars focus on the time delays systems. In order to describe the actual systems more accurately, the delay and the singular phenomenon must be considered simultaneously, which makes the research of time-delay nonlinear singular systems more theoretical and practical significance. In this thesis, H∞control problems for a class of nonlinear singular systems with time delays are studied. The main contents in the dissertation are as follows:(1) The development and application of the singular systems, robust H∞control and Hx filtering control are introduced, and the method-free weighting matrices that used in this thesis is introduced.(2) The definitions of stability of the singular systems, singular systems with time delays, the basic knowledge of H∞control theory, and some basic commonly mathematical inequalities used in this paper are introduced. These are the basis of this article.(3) The problems of H∞control for a class of time delays nonlinear singular systems and robust H∞control for a class of time delays nonlinear singular systems with uncertainties are studied repectively. First, by means of Lyapunov function, free weighting matrices is introduced, and the stability of the systems is analyzed. Based on which, a sufficient condition is presented such that the system is asymptotically stable and has a H∞norm constraint. Then the robust H∞controller is designed to guarantee the resulting closed-loop systems asymptotically stable and has a H∞norm constraint. The examples are given in the end correspondingly to prove the effectiveness of the conclusions.(4) The problems of H∞filtering control for a class of nonlinear singular systems with time delays are discussed. To estimate the output of the systems, an appropriate filters is designed. Utilize Lyapunov function, the stability of the closed-loop systems is analyzed. Based on it the sufficient conditions of asymptotic stability and the H∞norm constraint is given in this systems, then the sufficient conditions of the existence of the filter controller is given for the systems, and we design the corresponding filter, the final numerical examples illustrate our results.