The Structure of Determining Matrices for Single-Delay Autonomous Linear Neutral Control Systems

Abstract

This paper derived and established the structure of determining matrices for single – delay autonomous linear neutral differential systems through a sequence of lemmas, theorems and corollaries and the exploitation of key facts about permutations. The proofs were achieved using ingenious combinations of summation notations, the multinomial distribution,change of variables technique and compositions of signum and max functions. The paper also pointed out some induction pitfalls in the derivation of the main results. The paper has extended the results on single–delay models, with more complexity in the structure of the determining matrices.