Control design of switching systems by backstepping.

摘要

Switching systems are a particular class of hybrid system consisting of several dynamical subsystems with rules that determines the switching among them. Most references only dealt with continuous switching systems, especially the switching systems with subsystems of same "order". This assumption is restrictive and is not based on theoretical foundations but on mathematical convenience. This thesis proposes a backstepping approach to design stabilizing controllers for a broad class of nonlinear switching systems, which consist of strict feedback subsystems. By switching between sub-controllers, the backstepping-based controller can stabilize the unstable switching system or achieve asymptotic tracking. Meanwhile, the Lyapunov functions in quadric form are obtained simultaneously in the procedure of controller design. Based on the multiple Lyapunov function theorem, some sufficient conditions are given to guarantee the stability of closed-loop switching systems. Finally several examples are given and discussed to illustrate the theoretical results for both same-order and multiple-order switching systems.