Stabilization and L₂– Gain Performance of Periodic Piecewise Impulsive Linear Systems

This paper deals with the stability, stabilization and L
₂
- gain problem of periodic piecewise impulsive linear system. Firstly, by developing a new Lyapunov function called multiple piecewise time-varying Lyapunov function, a sufficient condition that guarantee the system λ* - exponentially stable is established. Moreover, a state-feedback controller is designed to stabilize the system. Then L
₂
- gain analysis is investigated to obtain a result that guarantee the system λ* - exponentially stable and with L
₂
- gain performance. Finally, numerical simulation examples are provided to verify the effectiveness of the results proposed in this paper.