Explicit (global) parametrization of all stabilizing compensators and observers for linear feedback systems

Abstract

An explicit global parametrization of all stabilizing feedback laws (guaranteeing the internal stability of the closed-loop system) and observers for a linear system defined over a field are developed. The global stabilizing compensators and observers are obtained as linear systems over rings of multivariable polynomials (in real variables, if the original system is defined over real numbers). Substitutions of certain values to these parameters yield the individual stabilizing compensators and observers. Explicit formulae are given, that require solution of only linear equations over the base field (e.g. real numbers) for the first time for the construction of such compensators and observers. The results are applicable to both direct dynamic output feedback configurations, and observer and state-feedback configurations. The results established here can be readily complemented by certain parameter optimization techniques in the literature to obtain a general purpose control system design technique that tak...