New delay-dependent stability criteria for linear time-delay systems with two additive time-varying delay components

This paper studies the stability problem for linear time-delay systems with two additive time-varying delay components. Based on Lyapunov stability theory and reciprocally convex lemma, a new delay-dependent stability criterion is obtained by considering the relationship between the two time-varying delays and their upper bounds. By using delay-dividing method, a further improved stability criterion is obtained. The obtained criteria are also extended to cope with the stability problem for this type of interval time-varying delay systems. All the obtained criteria are in terms of Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to show the effectiveness of the proposed method.