RANK EQUALITY OF CONTROLLABILITY MATRICES OF A CLASS OF DOUBLE-DELAY CONTROL SYSTEMS FOR FINITE AND INFINITE HORIZONS
UKWU CHUKWUNENYE *
Department of Mathematics, University of Jos, P.M.B 2084, Jos, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper aimed at obtaining some rank conditions on controllability matrices necessary for the investigation of Euclidean controllability of a class of double-delay control systems. The investigation was achieved by exploiting the novel relationships among the determining matrices, partial derivatives of the control index matrices and systems coefficients, as well as the application of the generalized Cayley-Hamilton theorem. This paper proved the equality of ranks of some concatenated determining matrices of a class of double-delay control systems for finite and infinite horizons which is an indispensible tool for the proof of the Euclidean controllability of the systems. The work has prepared the grounds for the investigation of Euclidean controllability of the aforementioned systems in a subsequent paper, by pioneering the introduction of the greatest and least integer functions in the proof of the equality of ranks of blocks of some concatenated matrices referred to as controllability matrices.
Keywords: Generalized Cayley-Hamilton theorem, concatenated matrices, double-delay control systems, horizon, systems