A SOS based alternative to LMI approaches for non-quadratic stabilization of continuous-time Takagi-Sugeno fuzzy systems

Nowadays, when dealing with non-quadratic controllers design for continuous-time Takagi-Sugeno (TS) models, LMIs-based successive conditions become more and more complex for a conservatism reduction that is sometime questionable. Therefore, in this paper it is assumed that it should be interesting to explore what can be done, else than LMIs, in the non-quadratic framework. Indeed, in most of the cases, non-quadratic LMIs suffer from the requirement of unknown parameters or lead to local stability analysis. Hence, the aim of this paper is to show, at a first attempt, that the Sum-Of-Squares formalism is suitable to design non-PDC controllers which stabilizing TS models on their whole definition set. However, it is pointed-out that the SOS formalism requires a restrictive modeling assumption, understood as a drawback but opening some possible further prospects.