Stability and $L_2$ Synthesis of a Class of Periodic Piecewise Time-Varying Systems

In this paper, the stability, stabilization, and L ₂ -gain problems are investigated for periodic piecewise systems with time-varying subsystems. Continuous Lyapunov function with time-varying Lyapunov matrix is adopted. A condition guaranteeing the negative definiteness of a matrix polynomial, deriving from the Lyapunov derivative, is first...