Robust Stabilization Analysis For A Class Of Nonlinear Singular Systems

Nonlinear system can be understand by differential equation describing system. For nonlinearsystem research and linear system research are almost at the same time.The ideal linear systems in factis practically non-existent. Nonlinear systems have a profound historical significance. In the recent20years, due to the nonlinear system in the study of introducing differential algebraic theory anddifferential geometry method,the development of mathematics of nonlinear analysis, nonlinearfunctional differential manifold and the nonlinear kinetics in physics promote the development ofthe nonlinear control theory. Nonlinear science got extensive attention from all walks of life, whichmakes the nonlinear control theory and application has a thriving development.In this paper,the development of the nonlinear system is firstly introduced.such as generalnonlinear system theory,robust stabilization andL₂gain.Further,the robust stabilization andL₂gainof nonlinear singular system are researched by robust stabilization andL₂gain of nonlinear system.（1）For a class of nonlinear singular system,the concept of robust stabilization is first introducedand research robust stability problem. Robust stability for nonlinear systems of the concept andmethod were generalized to the nonlinear singular systems.This paper studys the system feedbackrobust stabilization problem.The conditions under which the nonlinear singular system can realizefeedback stabilization were obtained. For regular nonlinear singular systems,with the system of vectorrelative degree and the normal form of the systems, the feedback control law was found in which thecorresponding closed loop systems can realize stabilization.（2）According to the regular nonlinear singular system,the concept ofL₂gain is firstlyintroduces,then,byL₂gain method of nonlinear system,the problem ofL₂gain is discussed.Theconditions ofL₂gain were obtained.