Robust stability analysis and controller synthesis for uncertain impulsive positive systems under L-gain performance.

This paper addresses the problems of robust stability analysis and L-gain controller synthesis for uncertain impulsive positive systems. First, by employing the idea of impulse interval partitioning, an impulse-time-dependent discretized copositive Lyapunov function is proposed to analyze the robust stability and L-gain performance of the considered system without control inputs, and several stability conditions and L-gain criteria are respectively derived. Subsequently, a sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust uniform asymptotic stability of the resulting closed-loop system are guaranteed, but also a prescribed L-gain performance is satisfied simultaneously.