Abstract
This paper deals with the problem of stability for continuous system with two additive time-varying delay components. By making full use of the information of the marginally delayed state, a novel Lyapunov–Krasovskii functional is constructed. When estimating the derivative of the Lyapunov–Krasovskii functional, we manage to get a fairly tighter upper bound by using the method of reciprocal convex and convex polyhedron. The obtained delay-dependent stability results are less conservative than some existing ones via numerical example comparisons. In addition, this criterion is expressed as a set of linear matrix inequalities, which can be readily tested by using the Matlab LMI toolbox. Finally, four examples are given to illustrate the effectiveness of the proposed method.
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