Nonquadratic Stabilization of Continuous T–S Fuzzy Models: LMI Solution for a Local Approach

Abstract

This paper is concerned with nonquadratic stabilization design problem for continuous-time nonlinear models in the Takagi-Sugeno (T-S) form obtained by sector nonlinearity approach. Most of the previous results found in the literature intended to establish global nonquadratic stabilization conditions which are hard to uphold due to the difficulty of handling time derivatives of the membership function. By changing the paradigm of global stabilization for something less restrictive, a local solution to overcome infeasible quadratic stabilization conditions is offered in this paper. It is shown that the derived local nonquadratic conditions actually lead to reasonable advantages over the existing quadratic approach, as well as some previous nonquadratic attempts. Moreover, conditions for the solvability of state feedback controller design given here are written in the form of linear matrix inequalities (LMIs) which can be efficiently solved by convex optimization techniques. Simulation examples are given to demonstrate the validity and applicability of the proposed approaches.