Disturbances rejection for fuzzy systems with time-varying delay and states constraints by applying observer-based invariant set switching

In this paper, the ability of disturbance rejection is considered for nonlinear systems presented by Takagi-Sugeno (T-S) fuzzy model with time-varying delay. First, a membership function dependent Lyapunov-Krasovskii functional is designed to handle the time-varying delay and an observer-based switching controller is designed to cope with the time derivative of membership function. For each switching signal, an invariant set is estimated corresponding to the switching controller, and the subset of the intersection is also an invariant set if the number of switching is finite with energy bounded disturbance. Then, for the trajectory starting from the origin, the ability of disturbance rejection is measured by H(infinity )performance and for other cases, two sets are designed such that any trajectories beginning with the smaller one will remain in the larger one. Finally, the merits of the proposed method are demonstrated by two examples.