A dynamic game approach to mixedH∞/H2 estimation

Abstract

A deterministic, two-person, zero-sum, linear quadratic estimation game, which is closely related to the mixed H∞/H2 estimation problem, is introduced. The strategy of the estimator in this game must guarantee a prescribed H∞-performance level γ. If the desired H∞-performance level is not achieved by an H2-optimal estimator, the H2-performance of the estimator must be degraded. An optimal estimator, in the sense of this game, minimizes the ratio between the resulting H2-performance degradation, and the performance degradation that would have been obtained if one had used the standard H∞-central filter. Both the continuous and the discrete-time cases are treated.