Quantised stabilisation of continuous-time switched systems with time-delay

This study is concerned with the problem of achieving exponential convergence and Lyapunov stability with respect to time-varying time-delay for switched systems with quantised measurements. Here the controller under the influence of time-delay is designed by quantised sampling signals to stabilise the continuous-time switched systems. The difficulty of this study lies in how to design a quantisation rule ensuring the unsaturation of quantiser under the coupling effect of switching uncertainty and time-delay uncertainty. To this aim, a virtual system is introduced to update observer States and facilitate stability analysis. Furthermore, by restraining the upper bound of the sampling interval, all the situations discussed are divided into three categories, under which, the authors study the distinguishments of system States and observer States at delay time to acquire quantisation rule and quantiser properties at the sampling time. Within this setup, the upper bound of the system States and thus the stability of the closed-loop systems are obtained. The authors at last give an illustrative example to show the usefulness of the proposed framework for stability analysis of some classes of switched systems.