Observer‐based controller design of discrete‐time piecewise affine systems

This paper presents a novel observer‐based controller design method for discrete‐time piecewise affine (PWA) systems. The basic idea is as follows: at first, a piecewise linear (without affine terms) state feedback controller and a PWA observer are designed separately, and then it is proved that the output feedback controller constructed by the resulting observer and state feedback controller gains can guarantee the stability of the closed‐loop system. During the controller design, the piecewise‐quadratic Lyapunov function technique is used. Moreover, the region information is taken into account to treat the affine terms, so the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically feasible with commercially available software. Three simulation examples are given finally to verify the proposed theoretical results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society