Non-fragile L2-L∞ control for Markov jump systems with general transition probabilities against multiple disturbances

This paper is concerned with the non-fragile L-2-L-infinity control problem of Markovian jump nonlinear systems. The considered transition probabilities are more general, which covers known case, uncertain case and unknown case. A disturbance generated by an exogenous system is estimated based on a disturbance observer to construct non-fragile state feedback controller with additive gain variations. Simultaneously, another kind of disturbance in L-2 [0, infinity) space is also been dealt with. The induced nonlinearity by uncertain transition probabilities has been solved based on a separated technique. Some sufficient conditions to guarantee the closed-loop system stochastically stable are obtained by using Lyapunov method and linear matrix inequalities technique. Finally, a single link robot arm model is used to illustrate the effectiveness of the proposed method