Reduced-Order Discrete-Time Recursive Observers for Linear Continuous-Time Singularly Perturbed Systems

A new technique for constructing decoupled reduced-order discrete-time slow and fast observers for singularly perturbed continuous-time linear systems with piecewise-constant inputs is presented. The resulting state estimates are shown to converge to a neighborhood of the true states, in the sense that the state estimation error vanishes as the singular perturbation parameter tends to sero. The reduced-order multirate implementation results in significant computational savings over competing full-order techniques. Moreover, in the event that the singular perturbation parameter is sufficiently small with respect to the input sampling period, a simplification can be made which further reduces the computational requirements.