Stability and L2-gain analysis of periodic piecewise linear systems

This paper investigates the stability and L₂-gain problems for a class of continuous-time periodic piecewise linear systems with possibly non-Hurwitz subsystems. First, the exponential stability of periodic piecewise systems is studied by allowing the Lyapunov function to possibly non-monotonically decreasing over a period. A sufficient condition is established in terms of matrix inequalities. In light of the proposed Lyapunov function, the L₂-gain criterion is derived for periodic piecewise linear systems as well.