Exponential stabilisation of delayed Lur'e systems with multi-rate sampled-data control

Abstract

In this paper, we focus on the multi-rate sampled-data based exponential stabilisation problem of delayed Lur'e systems. First, a merging time sequence is constructed from the sampling instants of multiple sensors to form the so-called analysis interval and the closed-loop system is represented by a system with multiple time-varying delays over the constructed analysis interval. Then, a useful estimation about the norm of the system state is established. On this basis, a stabilisation criterion is proposed by constructing a two-sided looped-functional. The proposed functional drops positive definite restrictions over the whole analysis interval . Therefore, it can reduce the conservatism of the derived criterion. And, the feasible solution of the multi-rate sampled-data controller gain can be provided by solving a set of LMIs. Finally, the given example shows the advantage of the main results.