Based On The The L_p Gain Of Nonlinear Systems Robust Control Method

Based on the structured Lp gain singular value method, this paper investigates the robust robustness analysis and synthesis problem of nonlinear system with structured uncertainty. The paper also views the nonlinear H- control problem with kinds of new standpoints, and discusses the internal relations between other gain problems and nonlinear H- problem.The robustness analysis and synthesis is based on the structured Lp gain singular value. According to the boundary property of the singular value, it is easy to obtain the robust stability theorem. This thesis has proven the upper bound property of singular value and robust stability theorem, and analyzes the conservatism influences. The obtained results show the conservatism is not only in relation to the structured traits of uncertainty, but also depended on the input of the system. The problems of robustness performance and robustness synthesis can be transformed into the robust stability problem. In this way, the robustness analysis and synthesis are unified. For a class of affine nonlinear system with structured uncertainty, the researches are based on the robustness stability and robustness performance theorem, and the results fs characterized as the nonlinear matrix inequality (NLMI).The thesis views the nonlinear H- control problem with kinds of new eyes. The obtained results indicate the passivity problem to a system can be transformed into a L2 gain problem to another corresponding system, and the Backstepping recursive design method is used to design such that a nonlinear system with especial structure is passive. It is obvious that the L2 gain problem is the special case of Lp gain problem, and this thesis has proved that every Lp gain problem is equivalent with others. The input-state stability(ISS) is a more general concept, it considers the case of nonlinear gains. The thinking viewing stability from ISS viewpoint is introduced. The last section considers the inverse optimal H- problem. Its solvability is the condition of stabilization, and it is not difficult to know, there are some internal relations between inverse optimal H- problem and the robust stability problem for the nonlinear system with structured uncertainty.