Impulsive stabilization of positive systems with time-varying delays

This study investigates the impulsive stabilization problem of positive systems with time-varying delays. A new time-varying weighted copositive Lyapunov function is constructed. Sufficient stabilization conditions on the upper and lower bounds of impulsive intervals are established using the convex combination technique. Under the proposed conditions, the positivity and exponential stability of the corresponding closed-loop system can be guaranteed. Based on the linear programming (LP) technique, a systematic design procedure is presented for the impulsive controller. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical result.