Sampled-Data Control for Asynchronously Switched Linear Systems Without MDT Constraints

Yang Li,Wenju Du,Xiaozeng Xu,Hongbin Zhang

doi:10.1109/access.2021.3131736

Abstract

In this paper, the sampled-data control problem is studied for asynchronously switched linear systems (SLSs) without minimum dwell time (MDT) constraints. The asynchronous phenomenon exists due to that the information of system mode can be acquired only at the sampling instant. First, a sufficient condition of global asymptotic stability (GAS) is presented for sampled-date switched control systems with a novel class of switching signals, which allows the switching number to be a non-affine function of time, and does not involve any point-wise bound on the switching number. Moreover, unlike the existing literature concerned with sampled-data control problem of switched systems, the MDT constraints are removed. We allow that no sampling happens between two adjacent switching instants, which makes the results more applicable to practice. Then, a sufficient condition checking the existence of sampled-data controllers is presented in terms of linear matrix inequalities (LMIs). Finally, it is shown by a boost converter circuit system that the designed sampled-data controller and switching signals can stabilize the system cooperatively.

Highlights

Switched systems consist of several subsystems and a switching signal selecting the activated mode at any constant
The main contributions are as follows: 1) Unlike the existing literature [26]–[35] concerned with switched systems’ sampled-data control problem, we do not require the minimum dwell time (MDT) of the switching signals to be larger than the maximum sampling interval, i.e., we allow that no sampling happens between two adjacent switching instants, which shows the results in this paper are more applicable to practice
With the help of the package YALMIP [42] and SDP solver SeDuMi [43], we find that feasible solutions for the conditions in Theorem 2 exist for h ≤ 1.32

Summary

INTRODUCTION

Switched systems consist of several subsystems and a switching signal selecting the activated mode at any constant. The main contributions are as follows: 1) Unlike the existing literature [26]–[35] concerned with switched systems’ sampled-data control problem, we do not require the MDT of the switching signals to be larger than the maximum sampling interval, i.e., we allow that no sampling happens between two adjacent switching instants, which shows the results in this paper are more applicable to practice.

SYSTEM DESCRIPTION AND PRELIMINARIES

SIMULATION

CONCLUSION