time delay

lyapunov functions

exponential stability

neural networks time-varying

delay systems

takagi sugeno

asymptotic stability

time-varying delays

delay differential

linear matrix

Applied Mathematics and Computation

This paper focuses on the delay-dependent stability problem of time-varying delay systems. A generalized free-matrix-based integral inequality (GFMBII) is presented. This inequality is able to deal with time-varying delay systems without using the reciprocal convexity lemma. It overcomes the drawback that the Bessel–Legendre inequality is inconvenient to cope with a time-varying delay system as the resultant bound contains a reciprocal convexity. Through the use of the derived inequality and by constructing a suitable Lyapunov–Krasovskii function (LKF), improved stability criteria are presented in the form of linear matrix inequalities (LMIs). Two numerical examples are carried out to demonstrate that the results outperform the state of the art in the literature.

A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems