Relative controllability and null controllability of linear delay systems with distributed delays in the state and control

Abstract

Necessary and sufficient conditions are established for the relative, absolute controllability and null controllability of the generalized linear delay system and its discrete prototype. The paper presents illuminating examples on previous controllability results by Manitius and Olbrot [7] and carries over the results of Onwuatu [8] and Klamka [4] to delay systems. It generalizes the results of Sebakhy and Bayoumi [11]. An algebraic approach is adopted in most of the proofs; while a manifestation of interest in the utilization of the asymptotic behaviour of solutions of differential equations provides computable criteria for relative null controllability of linear systems.

Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 221-238