New results of stability analysis for systems with two additive time-varying delays

This paper studies the problem of stability analysis for continuous-time systems with two additive time-varying delay components. By taking the independence and the variation of the additive delay components into consideration, a more general type of Lyapunov functionals is defined. Together with a tighter estimation of the upper bound of the cross-product terms derived from the derivative of the Lyapunov functional, a less conservative delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs). Combining with a reciprocally convex combination technique, the newly obtained stability conditions are also less complex. A numerical example is given to illustrate the effectiveness and the significant improvement of the proposed method.