Minimal Controllable Set for Takagi-Sugeno Fuzzy Systems with disturbances

Abstract

In this paper, an approximation of the smallest set (in a given norm) to which the state of a system can be steered (and kept inside once reached) is provided, when bounded disturbances are present. A non-LMI geometric polytope-manipulation approach is pursued over a Takagi-Sugeno model in order to solve this disturbance-rejection setup. Once this set is available, the techniques in this paper compute, too, explicit controllers driving initial conditions to such set, as well as controllers that make this set invariant. This work generalises the earlier particular undisturbed case (i.e., just stabilization) developed in Ariño et al. (2017b).