Stability and stabilisation of Markovian jump systems under fast switching: an averaging approach

Abstract

This paper addresses the problems of stability and stabilisation of Markovian jump systems (MJSs) with fast switching. First, a novel model by applying an averaging approach to the fast switching is proposed. Then, a new method for constructing an auxiliary system is given to make the stability analysis. It is proved that the stability of the originally fast switching MJS could be guaranteed by an MJS with an average switching, if the fast switching achieves its average approximation sufficiently fast. Based on the proposed results, some extensions about generally stabilising controllers are considered, where the fault-tolerant situation is involved too. All the conditions are presented in terms of LMIs. Finally, two numerical examples are used to demonstrate the effectiveness and superiority of the method.