Output feedback H∞ control for uncertain piecewise linear systems

This paper is concerned with the design of robust H(infinity) output feedback controller for uncertain piecewise-linear systems based on piecewise-quadratic Lyapunov function technique. We assume that the uncertainty is norm-bounded and enters all system matrices. By constructing piecewise-continuous Lyapunov function for the closed-loop augmented system, we construct the H(infinity) output feedback controller design procedure as solving a set of bilinear matrix inequalities (BMIs). The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities (LMIs) which can be efficiently solved numerically. A numerical example is used to illustrate the proposed method.