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

Qizhe Chen, Xia Huang, Lan Yao and Yuxia Li

International Journal of Systems Science, 2022, vol. 53, issue 15, 3190-3204

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 $ \{t_k\} $ {tk} 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 $ [t_k,t_{k+1}) $ [tk,tk+1). 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.

Date: 2022
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DOI: 10.1080/00207721.2022.2076173

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