New delay-dependent stabilization conditions of T-S fuzzy systems with time varying delay

Abstract

This paper deals with the problem of delay-dependent stability and stabilization of Takagi-Sugeno (T-S) fuzzy systems with a time-varying delay. A new method which brings three great advantages for the T-S delay-dependent stabilization problem is developed. The first one is that this method is less conservative than other existing ones. The second one is the reduction of computational complexity when the number of IF-THEN rules r is big. The third advantage the delay-dependent stabilization conditions presented involve a single tuning parameter. The stabilization conditions are derived using single Lyapunov-Krasovskii Functional (LKF) combining the introduction of free-single matrices. Review some results are used to make these conditions in term of Linear Matrix Inequalities (LMIs) (which can be easily solved using existing solvers such as the LMI Toolbox in Matlab). Two numerical examples are taken from the literature to show the advantages of the design procedures.