Saturated control for uncertain nonlinear impulsive systems with non-uniformly distributed packet loss

This article aims to provide a unified theoretical framework for studying the dynamic behavior of uncertain impulsive systems involving saturation structure and packet loss phenomenon. The concept named average packet loss interval (APLI) is developed to characterize the distribution of packet loss intervals. In this scenario, the traditional restrictions on the number, the proportion, or the upper bound of packet loss intervals can be significantly relaxed. By modeling the original systems as the asynchronous impulsive switched systems, some sufficient criteria are derived via the set invariant approach, addressing how to integrate the effects of impulsive and external disturbances into input-to-state stability (ISS) performance. It is also shown that the robustness of system performance against packet loss can be guaranteed ideally. Then, an optimization algorithm is designed with the hope of getting the maximum estimate of the domain of initial values. Finally, two examples are discussed to demonstrate the effectiveness of our proposed results.