Observer design for singular hybrid systems with its application to disturbance-observer-based control

Full-order disturbance-observer-based control for singular Markovian jump system with two types of disturbances is investigated in this paper. By assuming that the system states is unavailable, full-order observers for both system states and the disturbance with a nonlinear control scheme are constructed, such that, the composite system is stochastically admissible, and the two types of disturbances can be attenuated and rejected, respectively. Based on the Lyapunov stability theory, sufficient conditions are established for the existence of the desired full-order disturbance-observer-based controllers in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show the effectiveness of the proposed approaches.