Stability, stabilization and L2-gain analysis of periodic piecewise linear systems

In this paper, the stability, stabilization and L-2-gain problems are investigated for periodic piecewise linear systems, in which not all subsystems are Hurwitz. First, some sufficient and necessary conditions for the exponential stability are established. By employing a discontinuous Lyapunov function with time-varying Lyapunov matrix, stabilization and L-2-gain conditions of periodic piecewise linear systems are proposed by allowing the corresponding Lyapunov function to be possibly non-monotonically decreasing over a period. A state-feedback periodic piecewise controller is developed to stabilize the system, and the corresponding algorithm is proposed to compute the controller gain. The L-2-gain criteria with continuous time-varying Lyapunov matrix and piecewise constant Lyapunov matrices are studied as well. Numerical examples are given to show the validity of the proposed techniques. (C) 2015 Elsevier Ltd. All rights reserved.