Stability analysis for a class of time-varying delay linear systems based on delay decomposition method

In this paper, we consider the stability of a class of linear systems with a time-varying delay. By using delay decomposition method, the time-delay interval is decomposed into two sub intervals to construct a suitable Lyapunov-Krasovskii functional, and each term of the Lyapunov-Krasovskii functional do not need to be positive definite, the partial items of Lyapunov-Krasovskii functional are consider that as a whole to determine its positive definiteness. And then different integral terms obtained in Lyapunov-Krasovskii functional derivatives are treated separately by using specific integral inequality, convex combination principle and Jensen's inequality, respectively. Next, an improved stability criterion for a class of linear systems with a time-varying delay is given in the term of linear matrix inequalities (LMIs). Finally, an example is given to show the effectiveness of the proposed method.