Disturbance-observer-based control & ℋ∞ control for non-linear Markovian jump singular systems with multiple disturbances

This study addresses the Problem of composite hierarchical anti-disturbance control [disturbance-observer-based controllers (DOBC) and ℋ_∞ control] for Markovian jump singular systems with non-linearity and two types of disturbances (the first is generated by an exogenous system and the latter is norm-bounded). The authors´ attention is focused on the design of a disturbance observer to estimate the first disturbance, and then on constructing a composite hierarchical control scheme such that the solution to the composite system is unique and exists, the composite system can be guaranteed to be stochastically admissible, and different types of disturbances can be attenuated and rejected simultaneously. By constructing a proper stochastic Lyapunov-Krasovskii functional, sufficient conditions for the existence of the desired DOBCs are established. Finally, a numerical eEEExample is provided to show the effectiveness of the proposed approaches.