Non-quadratic local stabilisation for continuous-time Takagi-Sugeno fuzzy models: a descriptor system method

This study presents a descriptor system method to deal with the nonquadratic stabilisation design problem for continuous-time Takagi-Sugeno fuzzy models. Most of the previous results intended to establish global non-quadratic stabilisation conditions by bounding the time derivatives of membership functions (MFs). Those results are hard to uphold because of the difficulty of evaluating the bounds of MFs practically. By reducing global stabilisation goals via local considerations, new non-quadratic stabilisation conditions are proposed which remove the aforementioned difficulty. It is shown that the derived local non-quadratic stabilisation conditions actually lead to reasonable advantages over the existing quadratic approach as well as some previous non-quadratic attempts. Moreover, conditions for the solvability of controller given here are not only expressed as linear matrix inequalities, but also take advantage of the redundancy of descriptor system method to reduce computational requirement. Simulation examples are provided to demonstrate the validity and applicability of the proposed approach.