RobustH_∞Control For A Class Of Nonlinear Singular Systems

In recent years, the study of nonlinear systems has achieved good results, at the same time, nonlinear singular systems draw learners’attentions gradually. It began to be applied to practical projects, particularly in the power systems, economic systems, chemical processes. Nevertheless, the majority of the research was still in the nonlinear singular systems solvability and numerical solution areas. Comparing with other systems, it was found that we got a certain degree of development in disturbance decoupling, input and output decoupling and output tracking of nonlinear singular systems, but we got few results about systems stability, robustness, L2gain and H∞control, Therefore, further study of nonlinear singular systems is still very necessary. In actual systems, various constraints, disturbance and uncertainty is widespread, in order to achieve the high performance requirements of the systems, we need to consider all aspects of the systems, the possibilities are added to the systems constrains, so that the systems can be more widely used in engineering practice and played greater value.In this sis, the L2gain problem of nonlinear singular systems was studied at first. The definition of L2gain for the nonlinear singular systems was given. On the basic of nonlinear singular systems with L2gain theory, the prerequisites of L2gain for the nonlinear singular systems were given. Comparing with the proof of L2gain for the nonlinear systems, the proof of L2gain for nonlinear singular systems was given. Then the theories and methods for H∞control of the nonlinear singular systems were explored.With the theories and methods for L2gain of nonlinear singular systems, and combining with the "completion of the squares" method, the H∞control problem definition of nonlinear singular systems was given, the theorem of H∞control problem for the nonlinear singular systems was proposed and the proof was given. In practice, there existed many uncertainties and unpredictable factors, so that, in the last chapter of this paper, we studied the theories and methods of H∞control for uncertain nonlinear singular systems. With the mathematical theory and research methods of L2gain and H∞control derived from the first two chapters, the analytical methods of H∞control problems for uncertain nonlinear singular systems were given. On this basic, the research methods of H∞control problem for uncertain nonlinear singular systems with disturbance were given.