Further results on absolute stability of Lur׳e systems with a time-varying delay

In this paper, we focus on the problem of absolute stability of Lur׳e systems with time-varying delay and sector-bounded nonlinearity. An improved free-matrix-based inequality (FMBI) is derived. By using this inequality and the convex combination technique, some new delay-dependent absolute stability criteria are derived. These conditions are given in the term of linear matrix inequalities (LMIs) and accordingly can be readily solved and checked. Finally, a numerical example is solved using the proposed method to demonstrate the effectiveness and its improvement over existing ones.