Results on Uniqueness of Periodic Solution, Exponential Stability and Controllability Properties of Neutral Delay System
Dodi K. Igobi *
Department of Mathematics and Statistics, University of Uyo, Akwa Ibom State, Nigeria.
Jeremiah Atsu
Department of Mathematics and Statistics, Cross River University of Technology, Calabar, Cross River State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The variation of constant method is employed to evaluate the periodic solution of a linear neutral system with an input function. Uniqueness of the obtained solution is established and proved by utilizing the inversion theory on a perturbed differential operator. The exponential stability of the system equation and the computation of the maximum delay bound for the system to be asymptotically stable are analyzed using the resolvent matrix of the system equation. The controllability of the system is studied by the analyses of the linear ordinary control and the free control parts of the linear neutral system for properness, non-singularity of the gramian matrix, canonical form of the controllable matrix and the non zero/ pole cancellation of the transfer function matrix. Results obtained are employed on neutral delay model of a partial element equivalent circuit (PEEC) consisting of a retarded mutual coupling between the partial inductance to confirm the suitability of the test.
Keywords: Uniqueness, stability, controllability, resolvent matrix.