Stability analysis and L₁-gain characterization for impulsive positive systems with time-varying delay

This paper is concerned with the issues of stability analysis and L₁-gain characterization for impulsive positive systems with time-varying delay. To obtain less conservative results, the impulse interval partitioning idea is employed to construct an impulse-time-dependent discretized copositive Lyapunov-Krasovskii function. For the noiseless case, a delay-dependent criterion is derived to ensure the globally asymptotic stability of the concerned systems under a ranged dwell-time constraint. When external disturbances are taken into account, the proposed copositive Lyapunov–Krasovskii function is further employed to the L₁-gain analysis for the concerned system. The differential evolution algorithm is proved to be an effective alternative to solve the associated non-linear optimization problems, e.g., calculating the optimal L₁-gain and the allowable upper (lower) bound for the dwell-time. Three examples are provided to validate the effectiveness of the theoretical results, and some comparative studies with the Razumikhin's method are also given to illustrate the superiority of proposed approach.