Exponential stability of impulsive systems with random delays under sampled‐data control

Abstract

In this study, the exponential stability problem of impulsive system is investigated via sampled-data control in the presence of random time-varying delays and non-linear perturbations. In particular, the time delays are considered to be randomly time varying and they obey the Bernoulli distributions. The authors' main attention is focused on the design of a sampled-data controller to ensure an exponential stability for the closed-loop system. By extending the first- and second-order reciprocal convex approach, an efficient method called third-order reciprocal convex technique is used to manipulate the main results. Through the construction of a suitable Lyapunov–Krasovskii functional combined with input delay approach and Briat lemma, several delay-dependent sufficient conditions for the concerned system are derived in the form of linear matrix inequalities which can be readily solved by utilising the valid software packages. Some numerical examples are given to illustrate the effectiveness of the developed control technique.