Stability and stabilization of delayed fuzzy systems via a novel quadratic polynomial inequality

Abstract

The stability and stabilization problems of a class of Takagi-Sugeno(T-S) fuzzy systems with time-varying delay are concerned in this paper. By introducing the tunable parameter l, a novel quadratic polynomial inequality is proposed to reduce the estimation gap with previous work. Sequentially, an appropriate Lyapunov-Krasovskii functional(LKF) containing some new s-dependent integral terms is constructed, the delay-dependent stability condition is further improved by combining the generalized free-matrix-based integral inequality (GFMBII) with the proposed inequality. Finally, four typical numerical examples are carried out to demonstrate the validity and feasibility of the stability criterion and controller design method.