The structure of determining matrices for a class of double – delay control systems

Abstract

This paper derived and established the structure of determining matrices 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 proofs were achieved using ingenious combinations of summation notations, the multinomial distribution, the greatest integer function, change of variables technique and compositions of signum and max functions. The paper has extended the results on single–delay models, with more complexity in the structure of the determining matrices.