A survey on stability analysis of discrete-time piecewise affine systems

Abstract: Piecewise affine (PWA) systems are useful models for describing non-linear and hybrid systems. They also result from LTI systems subject to con-strained optimal control. Recently, stability analysis of PWA systems has received increased interest since it can help to obtain explicit feedback control laws of low complexity (Grieder et al., 2003b; Grieder and Morari, 2003; Grieder et al., 2004). A wide range of methods with varying degrees of conservativeness are available, for analyzing stability of PWA systems. This survey introduces the most promising existing methods and adapts them to discrete-time PWA systems. Specifically, we investigate the computation of common quadratic, common quartic, piecewise affine, piecewise quadratic and piecewise quartic Lyapunov functions using linear programming, semi-definite programming and sum-of-squares techniques. Subse-quently, the different methods are compared regarding the likelihood of finding a certificate of stability and computation run time. The objective is to provide the reader with a practical ‘recipe ’ for analyzing PWA systems. To this end, an extensive case study is performed. Copyright c©2005 IFA