Stability, stabilization and L2L2-gain analysis of periodic piecewise linear systems

In this paper, the stability, stabilization and L2L2-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 L2L2-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 L2L2-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.