Disturbance-observer-based l2-l control for discrete-time Markovian jump system

This paper considers the problem of anti-disturbance control for discrete-time Markovian jump systems with multiple disturbances. The controller is constructed via disturbance-observer-based control and l2-lN control. The disturbances are divided into two parts. One, in the same channel as the control inputs, is described by an exogenous system. The other is assumed to be bounded with an H2 norm. A disturbance observer is presented to estimate and reject the first-case disturbances for discrete-time Markovian jump systems, and an l2-lN control scheme is used to attenuate the secondcase disturbances. By using linear matrix inequalities, a solvable sufficient condition is developed. Finally, the effectiveness of the proposed control scheme is demonstrated via a numerical example.