Asynchronous Control for Discrete-time Switched Time-delay Systems with Mode-dependent Persistent Dwell-time

This paper deals with asynchronous control for discrete-time switched time-delay system with persistent dwell-time (PDT). The mode-dependent PDT switching is adopted, which is more general than average dwell time switching. Moreover, to deal with the mode-dependent delay in mode identification and signal transmission, the asynchronous phenomenon between controllers and subsystems is considered. A new mode-dependent Lyapunov function is constructed, which is suitable to the asynchronous PDT switching. Then, the sufficient condition for globally uniformly asymptotically stable (GUAS) of the discrete-time switched time-delay system is proposed. Further, the asynchronous controller and switching law are designed such that the closed-loop system is GUAS. Finally, an application example of water pollution is given to show the effectiveness of the proposed method.

Automated summary

This paper deals with the asynchronous control of discrete-time switched time-delay system, proposing a new mode-dependent Lyapunov function and designing an asynchronous controller and switching law to achieve globally uniformly asymptotically stable behavior.