Necessary and Sufficient Conditions for Controllability of Double-delay Autonomous Linear Control Systems

This article formulated and proved necessary and sufficient conditions for the Euclidean controllability of double-delay autonomous linear control systems, in terms of rank conditions on the controllability matrices. The proof was achieved by the exploitation of the structure of the determining matrices, the relationship among the determining matrices, the indices of control systems and system’s coefficients of the relevant system and an appeal to Taylor’s theorem as applied to vector functions.