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

Abstract

This paper presents the central finite-dimensional H_infinity filter for linear systems with measurement 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 problem to an H_2 (optimal linear-quadratic) filtering problem, using the technique proposed in [1]. Application of the reduction technique becomes possible, since the optimal filtering equations solving the H_2 (linear-quadratic) filtering problems have been obtained for linear systems with measurement delay. The paper presents the central suboptimal H_infinity filter for linear systems with measurement delay, based on the optimal H_2 filter from [35], where the standard H_infinity filtering conditions of stabilizability, detectability, and noise orthonormality are assumed. Finally, to relax the standard conditions, the paper presents the generalized version of the designed H_infinity filter in the absence of the noise orthonormality. The proposed H_infinity filtering algorithm provides a direct method to calculate the minimum achievable values of the threshold gamma, based on the existence properties for a bounded solution of the gain matrix equation. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for linear systems with state delay against the central suboptimal H_infinity filter available for linear systems without delays. The simulation results show a definite advantage in the values of the noise-output transfer function H_infinity norms in favor of the designed filter.