Relationships among determining matrices, partials of indices of control systems matrices and systems coefficients for single–delay linear neutral control systems.

Abstract

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 single – delay autonomous neutral linear differential systems through a sequence of lemmas, theorems and corollaries and the exploitation of key facts about permutations. The proofs were achieved using appropriate combinations of summation notations, multinomial distribution, change of variables techniques and deft deployment of skills in the differentiation of matrix functions of several variables.