Abstract
This paper investigates the stability, stabilization and L1-gain of linear periodic piecewise positive systems. The monotonicity of linear periodic piecewise positive systems is first studied. Then a time-varying co-positive Lyapunov function for periodic piecewise positive systems is employed and a sufficient condition for the asymptotic stability of the system is established. Based on the provided co-positive Lyapunov function and the sufficient stability condition, a state-feedback periodic piecewise controller to stabilize the system is formed and an upper bound of L1-gain of the system is given. Finally, numerical examples are given to illustrate the theoretical results.
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