Asynchronously Switched Control With Variable Convergence Rate for Switched Nonlinear Systems: A Persistent Dwell-Time Scheme

Abstract

This article explores the $H_{\infty }$ control problem based on convergence rate constraints for switched nonlinear systems under two types of asynchronous switching. First, this study investigates the variable convergence rate control issue for switched nonlinear systems. Combining the generalized pole placement idea and the Takagi–Sugeno fuzzy technique, a novel $H_{\infty }$ control criterion is proposed, specifically focusing on convergence rate constraints. In addition, employing the persistent dwell-time switching to model two asynchronous scenarios in switched systems: time-delayed switching and mismatched switching, where the maximum asynchronous delay is permitted to exceed the subsystems dwell time. According to this new criterion, a novel $H_{\infty }$ fuzzy controller is designed for switched nonlinear systems with asynchronous characteristics. It cannot only guarantee the asymptotic stability of the target closed-loop system but also precisely adjust the convergence rate of the system states, while also having certain anti-interference ability. Finally, numerical simulation and the tunnel diode circuit system control example prove the effectiveness of the method provided in this article.