Generalized H2 performance analysis of periodic piecewise systems

This paper analyses the generalized H2 performance for a class of continuous-time periodic piecewise linear systems with possibly non-Hurwitz subsystems. A sufficient criterion is proposed in terms of matrix inequalities by employing a time-varying Lyapunov function which is formulated with periodic a continuous linear time-varying Lyapunov matrix. The Lyapunov function deceases non-monotonically over a period. Also, by using a Lyapunov function with common decreasing rates respectively for all Hurwitz subsystems and all non-Hurwitz subsystems over their operating intervals, a simplified stability criterion is established. A numerical example is given to illustrate the effect and feasibility of the proposed techniques.