Alternative Optimal Filter for Linear State Delay Systems

Abstract

In this paper, the optimal filtering problem for linear systems with state delay over linear observations is treated using the optimal estimate of the state transition matrix. As a result, the alternative optimal filter is derived in the form similar to the traditional Kalman-Bucy one, i.e., consists of only two equations, for the optimal estimate and the estimation error variance. This presents a significant advantage in comparison to the previously obtained optimal filter [1], which includes a variable number of covariance equations, unboundedly growing as the filtering horizon tends to infinity. Performances of the two optimal filters are compared in example; the obtained results are discussed.

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

“…To the best authors' knowledge, this is the first paper which applies the reduction technique of [1] to classes of systems other than conventional LTI plants. Indeed, application of the reduction technique makes sense, since the optimal filtering equations solving the H 2 (mean-square) filtering problems have been obtained for linear systems with state [34,35] or measurement [36] delays. Designing the central suboptimal H ∞ filter for linear systems with measurement delay presents a significant advantage in the filtering theory and practice, since (1) it enables one to address filtering problems for LTV time-delay systems, where the LMI technique is hardly applicable, (2) the obtained H ∞ filter is suboptimal, that is, optimal for any fixed γ with respect to the H ∞ noise attenuation criterion, and (3) the obtained H ∞ filter is finite-dimensional and has the same structure of the estimate and gain matrix equations as the corresponding optimal H 2 filter.…”