Average dwell time condition of unknown switched linear systems with variable structure adaptive backstepping control

In this paper, we consider stabilization of switched linear systems with unknown parameters and unknown switching signals. It is well known that for a switched system with all stable subsystems, if the dwell time of the switching signal are long enough, then the system remains stable. When systems are unknown, the value of dwell time to preserve stability are usually implicit and only can be shown qualitatively. We propose a variable structure (VS) adaptive backstepping control to achieve the control goal for a class of unknown switched linear systems and with this design, the value of average dwell time (ADT) that is sufficient for system stability can be obtained explicitly and systematically for high relative degree cases. For the considered switched system with unknown parameters, unknown switching signals, and unknown switching time instants, we can guarantee output regulation and signal boundedness for the closed loop system with the proposed controller provided the ADT of the switching signal is greater than the derived value. An example is provided to validate the results.