Controller synthesis of continuous-time piecewise linear systems based on piecewise Lyapunov functions

This paper investigates the robust H_∞ static output feedback (SOF) controller design for a class of continuous time piecewise linear systems. The objective is to design a piecewise SOF controller guaranteeing the asymptotic stability of the resulting closed-loop system with a prescribed H_∞ disturbance attenuation level. Based on common/piecewise Lyapunov functions combined with Projection Lemma and some convexification techniques, some new results to the SOF controller design are developed for the underlying continuous-time piecewise linear systems. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically efficient with commercially available software. A simulation example is also given to illustrate the effectiveness of the proposed approaches.