Reduced-order H_∞ optimal filtering for systems with slow and fast modes

In this paper we present a method that allows complete time-scale separation and parallelism of the H_∞ optimal filtering problem for linear systems with slow and fast modes (singularly perturbed linear systems). The algebraic Riccati equation of singularly perturbed H_∞ filtering problem is decoupled into two completely independent reduced-order pure-slow and pure-fast H_∞ algebraic Riccati equations. The corresponding H_∞ filter is decoupled into independent reduced-order, well-defined pure-slow and pure-fast filters driven by system measurements. The proposed exact closed-loop decomposition technique produces many savings in both on-line and off-line computations and allows parallel processing of information with different sampling rates for slow and fast signals.