Control and estimation of piecewise affine systems - Xu, Jun (2008)
Piecewise affine (PWA) system is 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 by introducing several novel Lyapunov functions, including piecewise homogeneous polynomial Lyapunov functions, partition-dependent Lyapunov functions and vertex-dependent Lyapunov functions. These approaches lead to less conservative stability analysis than existing results. 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 are presented. We then turn to the control problems of discrete-time PWA systems. We design the state feedback control for PWA systems by incorporating partition information of the system and applying S-procedure in terms of LMI and BMI. H8 and generalized H2 control of PWA systems are also investigated. Parallel to the control problem, we also consider H8 and generalized H2 estimation using Luenberger type estimators for both continuous-time and discrete-time PWA systems. Finally, we take the Takagi-Sugeno fuzzy system as an application of PWA systems and derive the corresponding stability conditions and controller design approaches.