Stability of nonlinear impulsive systems with non-uniformly distributed packet loss

Abstract

This study focuses mainly on the stability of a class of nonlinear systems with impulsive disturbance. In particular, we consider the possible non-uniformly distributed packet loss phenomenon in the controller-to-actuator channel. This packet loss is described by a characterization scenario in the average sense, known as the average packet loss interval (APLI). In this scenario, an average allocation strategy between the number of impulsive sampling intervals and the length of packet loss intervals is established. This implies that the limitations on the proportion or the upper bound of packet loss intervals can be relaxed. A sampled-data control is put forward based on impulsive disturbance, which not only brings better control performance but also reduces conservatism. In view of the Halanay inequality, the number of subsystem switchings caused by packet loss is allowed to be arbitrary. Based on the elastic constraint relationships established between system parameters and APLI, a series of conditions guaranteeing the globally uniformly exponential stability (GUES) are provided. Further, the admissible packet loss intervals can be estimated on an average basis by solving an algebraic inequality. Finally, a numerical example is discussed to demonstrate the validity of our study.