Control and estimation of piecewise affine systems

Abstract

Piecewise affine (PWA) system has wide applications in circuit and control systems. It is considered as a powerful tool to study nonlinear systems, as well as switched and hybrid systems. This thesis presents our research findings in control and estimation of PWA systems. We begin with the examination of the stability of PWA systems. We introduce a piecewise homogeneous polynomial Lyapunov function approach to achieve less conservative stability conditions by using two types of power transformations. Both continuous-time and discrete-time PWA systems are considered. The approach leads to less conservative stability analysis than existing results. In addition to these stability results based on halfspace representation, we also find ways to address the stability of PWA systems based on vertex representation. Specifically, we incorporate vertex information of local partition and utilize parameterized Lyapunov functions to deduce less conservative conditions for stability. Next, we address the controllability and reachability of a class of PWA systems. Based on a general classification method, explicit necessary and sufficient conditions in terms of system parameters for controllability and reachability are presented. We show that controllability and reachability can be asserted in finite steps in some situations. We also briefly discuss the general cases. We then turn to the controller design problems for discrete-time PWA systems. We first consider the state feedback control for PWA systems. By incorporating partition information of the system and applying S-procedure, linear matrix inequality ii ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library