H∞ filtering for systems with time-varying delay satisfying a certain stochastic characteristic

This study proposes a class of H_∞ filter design for linear time-delay system. The time delay considered here is assumed to be satisfying a certain stochastic characteristic. Corresponding to the probability of the delay taking value in different intervals, a stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the information of the probability distribution. Then new criteria is derived for the filtering-error systems, which can lead to much less conservative analysis results. It should be noted that the solvability of the obtained criteria depend not only on the size of the delay, but also the probability distribution of it. At last, numerical examples are given to demonstrate the effectiveness and the merit of the proposed method.