Observer theory

The paper is devoted to a comprehensive exposition of the theory of partial state observers in the state space context and the elucidation of the connection between this theory and the theory of observers in the behavioral context, as developed in [M.E. Valcher, J.C. Willems, Observer synthesis in the behavioral framework, IEEE Trans. Aut. Contr. 44 (1999) 2297-2307]. For this we use several techniques, including geometric control theory, polynomial and rational models, shift realizations, coprime factorizations, partial realizations and the basic results on behaviors and behavior homomorphisms. A connection between observers and the construction of state maps is made. (C) 2007 Elsevier Inc. All rights reserved.