BIBO stabilisation of continuous-time Takagi–Sugeno systems under persistent perturbations and input saturation

This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi–Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum ^*-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum ^*-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.