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

This paper presents the central finite-dimensional H∞ filter for linear systems with measurement delay, that is suboptimal for a given threshold γ 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∞ filtering problem to an H2 (optimal mean-square) filtering problem, using the technique proposed in [1]. Application of the reduction technique becomes possible, since the optimal filtering equations solving the H2 (meansquare) filtering problems have been obtained for linear systems with measurement delay. The paper presents the central suboptimal H∞ filter for linear systems with measurement delay, based on the optimal H2 filter from [36], where the standard H∞ 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∞ filter in the absence of the noise orthonormality. The proposed H∞ filtering algorithm provides a direct method to calculate the minimum achievable values of the threshold γ , 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∞ filter available for linear systems without delays. The simulation results show a definite advantage in the values of the noise-output transfer function H∞ norms in favor of the designed filter.