Variable structure model reference adaptive control of unknown switched linear systems with relative degree greater than one

Abstract

In this paper, we consider the model reference adaptive control (MRAC) problem of switched linear systems in which the parameters and switching time instants are all unknown. We apply the output feedback variable structure (VS) based adaptive controller to switched linear systems with general relative degrees and show error convergence and signal boundedness properties by multiple Lyapunov functions. Specifically, a sufficient condition on the switching signal is obtained to ensure stability and error convergence of the system. Incidentally, the robustness and performance of VS adaptive controllers of the systems with jump parameters, which are only seen by simulations in existing literatures, are shown by thorough theoretical analysis. Simulation results are provided to validate the analysis.