A Class Of Nonlinear Systems Based On The Bounded State Feedback Robust Stabilization Problem

This paper discusses the robustly stabilitable problem for a class of nonlinear systems based on bounded state feedback control laws, and mainly solves two problems: Singular H∞ control problem for a class of nonlinear discrete-time systems with a bounded-controller, and Robustly stabilitable problem for a class of nonlinear feedforward systems.In section 2 we mainly discuss the singular H∞ control problem for a class of nonlinear discrete-time systems with a bounded feedback control law. When the systems don't satisfy the regular condition, we attain our aim by dividing the regular part and the non-regular part. Firstly we get a necessary condition for the solvability of singular H∞ control problem for nonlinear discrete-time systems with a bounded-controller.Secondly a sufficient condition for the solvablitity of singular H∞ control problem for nonlinear discrete-time systems with a bounded-controller is given. The bounded controller we attain can let the closed-loop systems reach disturbing decay in the condition of internal stability.In section 3 we mainly discuss robustly stabilitable problem of a class of feedforward nonlinear systems with saturation function. In this section we use a nested saturation stabilizer to make a class of feedforward nonlinear systems globally stable. Here we show a universal controller can be used to solve the problem of global stabilization for a class feedforward systems that cannot be adequately controlled using existing methods. This part concludes the following main results. Some lemmas and their proofs are given firstly which are necessary to show system stable. Finally we address that the system is exponent convegence.