Stability Study Of Time-delay Systems Based On Double Wirtinger Type Integral Inequalities

Time delay exists in many practical systems such as networked systems, chemical systems, sensor networks, communication systems and economic systems. In practical engineering applications, linear time delay systems and neutral systems are not only both the most common time delay systems, but also the basis for investigating other types of time delay systems. This study focuses mainly on the problem of the stability analysis for linear time-delay systems and neutral type systems. The main contents of this paper are as follows:(1) The stability of interval time-varying delay systems is revisited. Based on the Lyapunov stability theory, an appropriate Lyapunov functional is constructed. By using a double Wirtinger-based integral inequality combined with the first-order and second-order reciprocal convex methods, a new stability criterion is derived in terms of linear matrix inequality(LMI). Numerical examples are given to show the merits of the present results.(2) The stability of neutral type systems with interval time-varying delay is studied. Based on the above method, new delay-dependent conditions for the stability test are given in terms of LMIs. Combined with the neutral system transformation method, the results are extended to the generalized state-space systems with time delays.Finally, conclusion is summarized, and the future work is proposed in the light of the problems in the research.