This paper presents a new result on \(H_{\infty }\) filtering criterion for delayed linear systems based on improved techniques. First, a proportional-integral-type exponential-based filter is proposed by introducing an exponential decay term, which unifies the Luenberger-type filter and the traditional proportional-integral-type filter as its special cases. As a result, the convergence rate of the filtering error system can be accelerated. Second, to facilitate the use of more information about time delays, a binomial formula-based functional is constructed by applying the binomial theorem. Consequently, the upper bound of the time-derivative of the Lyapunov-Krasovskii functional can be more accurately estimated, then some sufficient conditions that guarantee the existence of \(H_{\infty }\) filters for delayed linear systems are obtained. Finally, simulations are provided to demonstrate the effectiveness of the proposed method.
