Disturbance rejection of T–S fuzzy systems: a membership function-dependent EID method

The disturbance rejection problem of T–S fuzzy systems is concerned. Since the T–S fuzzy system is characterised by its membership function, less conservative stabilisation conditions can be derived from membership function-dependent Lyapunov function which contributes to the improvement of disturbance rejection performance. Specifically, we utilise a configuration composed of a membership function-dependent state observer for the state estimation, a membership function-dependent equivalent-input-disturbance estimator for the estimation and compensation of disturbance and an internal model for the reference tracking. It is revealed that this membership function-dependent Lyapunov function naturally leads to control gains switching in accordance with the derivative signs of the normalised premise variables. The switching rules and the design conditions for all control gains are obtained explicitly. In particular, the free-weighting-matrix approach is used to lessen the conservatism in the stability condition. Moreover, a concrete procedure for the controller design including the switching rule is given. Finally, the developed method is tested via simulations. The advantage of the membership function-dependent equivalent-input-disturbance method is validated by comparing with conventional methods.