H∞ model reference adaptive control of switched linear systems based on multi-time-varying Lyapunov functions

In this paper, the $ H_{\infty } $ H∞ model reference adaptive problem of a class of switched linear systems with parameter uncertainty under the switching of dwell time is studied. First, in the absence of interference, a time-varying Lyapunov function with increasing coefficient is introduced to derive sufficient conditions for the reference adaptive control of the $ H_{\infty } $ H∞ model, where the dwell time is an arbitrary preset constant. Secondly, an adaptive controller and adaptive law are proposed to ensure the asymptotic tracking of the switched system. Then, in the case of interference, the sufficient conditions for the solvable $ H_{\infty } $ H∞ model reference adaptive tracking control under dwell time switching are proposed, and the standard $ L_2 $ L2-gain performance of the switching system is analysed. The characteristic of this paper is to solve the $ H_{\infty } $ H∞ model reference adaptive tracking control problem of a class of switched systems with uncertain parameters by using time-varying Lyapunov function with increasing coefficient. The increasing coefficient in Lyapunov function can increase the degree of freedom of controller design and improve the control performance of the system. Dwell time switching can avoid the $ H_{\infty } $ H∞ control problem of switched system which cannot realise state-dependent switching because all state information cannot be obtained.