LMI-based H∞ control scheme for discrete-time piecewise affine systems

This paper presents an H
∞
state feedback controller design method for discrete-time piecewise affine (PWA) systems based on a piecewise quadratic Lyapunov function, and the partition information of the PWA systems is taken into account to reduce the design conservatism. Each polytopic operating region is outer approximated by a union of ellipsoids, then the minimum problem of the H
∞
performance index for PWA systems can be cast as a convex optimization problem involving linear matrix inequalities, which can be solved very efficiently. A simulation example is also given to illustrate the advantage of the proposed approach.