SERIES EXPANSION OF SINGULARLY PERTURBED LINEAR SYSTEMS WITH APPLICATIONS TO ESTIMATION.

Conditions are derived under which the slow modes of a singularly perturbed linear system have a lower-order slow-sampled series expansion. Initially, general linear systems with white noise inputs are considered, with the theory being later applied to state estimation problems. The implication to the filtering problem is that an estimator, with no greater complexity than the reduced filter, can be designed that approximates the slow modes much more closely, for larger values of the perturbation parameter. The conditions, which restrict the interconnections of the fast modes and the slow subsystems, are obtained as simple state and output controllability tests for time-invariant systems. Finally an example is provided to illustrate the simplicity of implementation and improvement in performance of this approach.