Counterpart of Advanced TS discrete controller without matrix inversion

This paper aims to present a systematic methodology for designing a Counterpart of an Advanced Takagi-Sugeno (CATS) discrete controller. Advance controllers for nonlinear systems under Takagi-Sugeno representation have been designed for years using efficient control laws such as the non-PDC (Parallel Distributed Compensation) controller. In terms of stabilization, that kind of controllers is a powerful tool which allows outperforming the classical PDC results using non quadratic Lyapunov function. However, in spite of these advantages, this control strategy presents a major inconvenient from real time implementation point of view: the use of a nonlinear matrix inversion at each sample time. In order to solve this problem, our paper presents a CATS controller design methodology to obtain an equivalent to the non-PDC controller without matrix inversion. Through a given procedure associated with a stability analysis, not only the efficiency is proved but also its validity. Finally, some simulation results will emphasize the originality and the usefulness of the proposed CATS controller.