Local Sliding Mode Control Design for T-S Fuzzy Systems with Magnitude and Rate Limited Input

This work focuses on the sliding mode control (SMC) for a class of T-S fuzzy systems subject to input saturation including bounded magnitude and rate. As the fuzzy model is valid only in the modeling region, it makes more sense to consider the local stabilization of the controlled system. A key issue is how to design an SMC law under the magnitude and rate constraints. To this end, an augmented fuzzy system is firstly developed, in which the input rate can be regarded as an auxiliary control variable. The actual control law is subsequently synthesized as the sum of this auxiliary controller and the actual control at the previous instant. Based on an ellipsoid set, the domain of attraction (DA) is estimated, from which the states originating can remain in the pre-specified modeling region. The magnitude and rate constraints can be guaranteed by converting these constraints into matrix inequalities. Furthermore, sufficient conditions are derived to achieve the local stability of the closed-loop system and the reachability of the prescribed sliding surface. A simulation example illustrates the proposed control method.