Reachability of a Class of Infinite-Dimensional Linear Systems: An External Approach with Applications to General Neutral Systems

Abstract

This paper studies the question of quasi- (approximate) reachability of the standard observable realizations of pseudorational impulse responses introduced by the author. The framework places the current theory of retarded and neutral delay-differential systems into a unified input/output framework. Several necessary and sufficient conditions for quasi-reachability are derived. In particular, new criteria for quasireachability and eigenfunction completeness are obtained for general delay-differential systems with no restriction on the type of delays. Furthermore, as a byproduct, the theory leads to necessary and sufficient conditions for approximate left coprimeness of matrices with distribution entries. Examples are discussed to illustrate the theory.