Adaptive control for time-delay Markovian jump linear systems with state-dependant switching

In this note, we investigate exponential mean-square stability for a class of time-delay Markovian jump linear systems with state-dependant switching. By solving a set of linear matrix inequalities (LMIs), a state-feedback nonlinear controller is obtained, which guarantees globally exponential stability of such systems in the mean-square sense. Based on this, an adaptive state-feedback control law is then designed with less knowledge of the state-dependent generator. An illustrative numerical example is provided to demonstrate the validity of the proposed approach.