Model Reference Adaptive Control for Switched Linear Systems With Uncertain Parameters and Its Application in Electro-hydraulic Systems

This paper studies the model reference adaptive control for a class of switched linear systems with uncertain parameters under the dwell time switching. Firstly, the sufficient conditions for the model reference adaptive control synthesis are derived by introducing the time-varying Lyapunov function with increase coefficient in the framework of dwell time technique, where the dwell time is an arbitrary prespecified constant. Secondly, an adaptive controller is proposed to ensure that the state of the switched system asymptotically track the state of the reference switched system. Thirdly, based on the Lyapunov function proposed, the lower bound of dwell time is restricted, the decrease of Lyapunov function between two consecutive switched times of the active subsystem is limited, the energy of the whole switched system is reduced, and the asymptotic stability of the error system is realized. Then, if the reference is persistently exciting, the closed-loop error system is asymptotically stable and the parameter estimation error asymptotically converges to zero. Finally, an electro-hydraulic system is taken as an example to verify the effectiveness of the proposed method.