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Home  >  Volume 27 (July 2014)

8. Interactions Amongst Determining Matrices, Partials of Indices of control Systems Matrices and Systems Coefficients for a Class of Double – Delay Control Systems by Ukwu Chukwunenye. Volume 27,(July 2014), pp 49 – 60
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This paper obtained various relationships among determining matrices, partial derivatives of indices of control systems matrices of all orders,as well as their relationships with systems coefficients for a class of double – delay autonomous linear differential systems through a sequence of lemmas, theorems, corollaries and the exploitation of key facts about permutations. The utility of these relationships is for the most part, in the investigation of Euclidean controllability.
 The proofs were achieved using ingenious combinations of summation notations, the multinomial distribution, greatest integer functions, change of variables techniques and deft deployment of skills in the differentiation of certain matrix functions of several variables.