Robust Passivity Of Nonlinear Systems In Nested Lower Triangular Structure

In this paper, an extended robust passive backstepping design procedure isproposed for a class of multi-input nested lower triangular nonlinear systems withuncertainties. That is, a feedback control law can be constructed to ensure the internalstability and passivity of the corresponding closed-loop system. The feedbackequivalence between the considered systems and passive systems is established byusing backstepping technique recursively. The sufficient condition for the systems tobe robust passive is achieved with the aid of Lyapunov stability theory and robustKYP lemma. The results will be summarized as follows:(1) The development, background and research technique of passivity of nonlinearsystems are introduced. We introduce some basic concepts and the results of theaffine nonlinear system, the robust passive and robust KYP lemma of nonlinearsystem with uncertainties.(2) The passivity of a class of nonlinear systems in nested lower triangular structureis researched. The sufficient conditions for the systems to be passive are given bycoordinate transformation, and the design method of the passive feedback controllaws is presented.(3) We also research the robust passivity of a class of nested lower triangularstructural nonlinear systems with uncertainties. Based on the effective restriction ofuncertainties, this system is proved to be feedback equivalence to a robust passivesystem. Finally, the robust passive feedback control law is presented.(4) Finally, we summarize the major work of this dissertation.