Finite-Dimensional H infinity Filter Design for Linear Systems with State Delay

Abstract

This paper presents the central finite-dimensional H_infinity filters for linear systems with state delay, that is suboptimal for a given threshold gamma with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the results previously obtained for linear time delay systems, the paper reduces the original H_infinity filtering problems to H_2 (optimal mean-square) filtering problems, using the technique proposed in [1]. The paper first presents the central suboptimal H_infinity filter for linear systems with state delay, based on the optimal H_2 filter from [33], which contains a finite number of the filtering equations for any fixed filtering horizon, but this number grows unboundedly as time goes to infinity. To overcome that difficulty, the alternative central suboptimal H_infinity filter is designed for linear systems with state delay, which is based on the alternative optimal H_2 filter from [34]. Numerical simulations are conducted to verify performance of the designed central suboptimal filters for linear systems with state delay against the central suboptimal H_infinity filter available for linear systems without delays.