Dynamic adaptive control of Markov jump systems with mixed transition rates through reduced-order sliding mode technique with application to circuits

The paper proposes an adaptive controller design for Markov jump systems with mixed mode transition information through a reduced-order sliding mode approach. The stability criteria and mode-dependent adaptive control law are achieved using linear matrix inequality technique. Firstly, a linear reduced-order sliding surface function is proposed to achieve the reduced-order sliding mode dynamics. Secondly, a feasible approach is presented to check the stochastic stability of resulting sliding motion corresponding to different mode transition information, and to solve the controller gains from stability criteria. Thirdly, an adaptive sliding mode controller is also designed to ensure the finite-time reachability of the predefined hyperplane even when no mode information is available. Finally, the application of the proposed control strategy to the RLC circuit is provided.