H∞Delay Filters Design for Linear Time-Varying Delay Systems in the Finite Frequency Domain: An Input-Output Approach
针对线性时变时滞系统，提出一种基于输入输出方法的H∞延迟滤波器设计，在有限频率范围内抑制外部干扰，并通过数值算例验证了优于现有方法。
This work focuses on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for linear time-varying delay systems. A new delay-dependent condition, equivalent to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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.