Asynchronous H_∞ Control of Switched Systems and Its Applications: An Admissible Chain-Dependent Average Dwell Time Switching Strategy

This work is interested in the stability analysis and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> control for a class of continuous-time switched systems with external disturbances and asynchronous switching. Based on the attributes of the closed-loop switched systems with edge-dependent state-feedback controllers, a novel admissible chain-dependent average dwell time switching strategy is proposed. The new switching is characterized by admissible transition chains derived from combining two admissible transition edges associated with two consecutive switching events, and it is expected to relax the dwell time constraints in the existing admissible edge-dependent average dwell time switching. Moreover, to reflect the nature of the discussed asynchronously switched systems, a hybrid chain- and edge-dependent Lyapunov function is introduced. Through the suggested switching and Lyapunov function methods, the stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula>-gain analysis results are obtained, based on which the intended edge-dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> control scheme is designed. Finally, the provided control scheme is validated through switched DC motor and Boost models as well as a numerical example. Note to Practitioners—Switched systems are powerful tools for modeling engineering systems with switching events. In practical switched applications, recognizing subsystem modes and applying matched controllers can take some time, which leads to the asynchronous phenomenon. Furthermore, external disturbances are unavoidable in real systems. The more relaxed dwell time constraints of switching signals mean better applicability of the obtained results, especially for switched systems subject to asynchronous switching and external disturbances. The disturbance attenuation performance of an asynchronously switched system can be improved by reducing the running time of the subsystem performing poorly on this performance. Therefore, it is meaningful to devise a control scheme with relaxed dwell time constraints, which can be resolved by our proposed edge-dependent control method with admissible chain-dependent average dwell time.