Stability Of Linear Delay Systems

In this paper, stability of linear system with time-varying delays are con-sidered. Firstly, general time-delay systems in three different situations of stability are considered by using the Lyapunov-Krasovskii approach and on Finsler's projection Lemma. One contains neither control input nor distur-bance vector, another only includes the control input not to contain the per-turbation and the third only includes the random disturbance not to include the control input. Next, according to the three cases, stochastic stable con-dition of linear system with two time-delays is presented.At the end, stability of system with time-varying delay and Markov jump is discussed. The stochastic stability is obtained by a linear matrix inequality, and stochastic stable sufficient condition is given.