Parameter-dependent Lyapunov function approach to robust L2–L∞L2–L∞ filter design for uncertain time-delay systems

An LMI-based method for robust L2–L∞L2–L∞ filter design is proposed for polytopic uncertain time-delay systems using a parameter-dependent Lyapunov function approach. Based on a new characterization, a strict LMI condition for L2–L∞L2–L∞ filter design is obtained, which does not involve any iterations for design parameter search, any couplings between the system matrices and the Lyapunov function matrix, nor any system-dependent filter parametrization. Therefore, the proposed condition enables us to easily employ, with the help of efficient numerical solvers, a parameter-dependent Lyapunov function approach to robust L2–L∞L2–L∞ filter design for uncertain time-delay systems. A numerical example is presented to show the effectiveness of the proposed method.