H∞Delay Filters Design for Linear Time-Varying Delay Systems in the Finite Frequency Domain: An Input-Output Approach

This work focuses on the $H_{\infty }$ filtering problem for linear time-varying delay systems. A new delay-dependent condition, equivalent to the $H_{\infty }$ inequality within a finite frequency range, has been established. A delay filter system is proposed to estimate the system’s output, aiming to minimize the impact of exogenous inputs on the outputs. The proposed methodology captures $H_{\infty }$ performance within a finite frequency range while maintaining input-output stability by employing a two-term approximation model and the Lyapunov–Krasovskii functional. The innovation lies in addressing the limitations of existing $H_{\infty }$ criteria, through a delay-dependent condition based on an input-output approach. The derived conditions are formulated as linear matrix inequalities. Numerical examples are provided to validate and illustrate the effectiveness of the proposed method, demonstrating its superiority over existing approaches in the literature.