Equivalences among Model Reduction, Filter-Observer and Feedback Control Design

Summary

The problems of model reduction, filter-observer and feedback control design in linear systems when treated from the parameter optimization point of view are shown to be mathematically equivalent under a wide variety of conditions. The common basis is an optimization problem of a scalar criterion with a Lyapunov equation side constraint, called the canonical problem. Aside from the conceptual advantage of showing that a wide variety of design concepts and techniques are mathematically equivalent, the canonical formulation provides a compact set of necessary conditions for the solution from which known and new results can be easily derived. Finally it also permits development of one general purpose program to handle many different objectives, criteria, and types of disturbances.