Robust H∞ filter design for linear time-varying delay systems via the Razumikhin technique

A new method of designing a robust H
_∞
filter is proposed for a class of linear time-varying delay systems by the Razumikhin technique. Razumikhin-type theorems for the robust H
_∞
filter which guarantees that the filter error system is globally asymptotic stability and satisfies the prescribed H
_∞
performance requirement when the system is affected by external disturbances, are established respectively. Among them, the stability condition is achieved by the fact the a delay system will keep stable if the time delay is small enough under the condition that the nominal system of the original system is stable. And the gain of the robust H
_∞
filter could be obtained by appropriate pole configuration under the condition that the nominal system of the original system is observable. The effectiveness of the proposed design method of the robust H
_∞
filter is demonstrated by a numerical example.