H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.