Adaptive stabilisation of random systems with arbitrary switchings

This study is concerned with the global stabilisation problem for a class of random non-linear systems with arbitrary switchings and parameter uncertainties. Under some milder assumptions and by constructing a Lyapunov function, a common adaptive state feedback controller is designed such that the resulting closed-loop system has a globally unique and almost surely bounded solution. Furthermore, the system states are exponentially noise-to-state stable in mean square. Finally, the efficiency of the proposed design approach is demonstrated by a numerical example.