Alternative Optimal Expressions for the Structure and Cardinalities of Determining Matrices for a Class Of Double – Delay Control Systems

Abstract

This paper exploited the results in Ukwu [1] to obtain the cardinalities, computing complexity and alternative optimal expressions for the determining matrices of a class of double – delay autonomous linear differential systems through a sequence of theorems and corollaries and the invocation of key facts about permutations. The paper also derived a unifying theorem for the major results in [1].The proofs were achieved using ingenious combinations of summation notations, the multinomial distribution, and greatest integer functions, change of variables techniques and compositions of signum and max functions. The computations were mathematically illustrated and implemented on Microsoft Excel platform for some problem instances.