Variable structure adaptive backstepping control for a class of unknown switched linear systems

In this paper, we consider adaptive control of switched linear systems with unknown parameters and unknown switching signals. Variable structure (VS) adaptive backstepping control with tuning function for relative degree one case is discussed. The parametrization of tuning function scheme leads the switched system into a non-switched one with a step change in the input channel and thus the stability properties are derived independent of the switching signal. Moreover, a VS adaptive backstepping control to switched linear systems with relative degree one and two are also proposed. Output error convergence and signal boundedness properties are derived by multiple Lyapunov functions. With the proposed VS adaptive backstepping controller, if the switching signal satisfies the average dwell time conditions, then the output error will converge to a designed residue set and all signals will be bounded. Some simulation results are provided to validate the analysis.