Euclidean Controllability of Linear Systems with Delayed State and Control Variables
Adiela Chukwumela *
Department of Mathematics, Rivers State University, Port-Harcourt, Nigeria.
Davies Iyai
Department of Mathematics, Rivers State University, Port-Harcourt, Nigeria.
Adols Okechukwu Nwaoburu
Department of Mathematics, Rivers State University, Port-Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper presents results on controllability of solution and control for linear systems with delay in control and state variables. Necessary and sufficient conditions for controllability using Kalman’s rank criterion for controllability are considered. If the uncontrolled system is uniformly asymptotically stable and the control equation is proper, then the control system is Euclidean null-controllable. Examples are given to illustrate the effectiveness of the theoretical results.
Keywords: Controllability, linear systems, null-controllablility, stability, dynamical systems