Composite DOBC & H∞ control for Markovian jump nonlinear systems

The problem of composite disturbance-observer-based control (DOBC) and H∞ control for Markovian jump systems with nonlinearity and multiple disturbances is investigated in this note. Two types of disturbances are considered, one is norm-bounded, and the other can be described by a linear exogenous system. Our aim is to design a disturbance observer to estimate the disturbance generated by an exogenous system, then construct the control scheme by integrating the output of the disturbance observer with state-feedback control laws, such that, the closed-loop system can be guaranteed to be stochastically stable, and different types of disturbances can be attenuated and rejected. By constructing a proper stochastic Lyapunov-Krasovskii functional, sufficient conditions for the existence of the desired observers gains and the state-feedback controller gains are established in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the proposed approaches.