Stability and Feedback Control of Volterra Type Systems with Time Delay
I. Davies *
Department of Mathematics, Rivers State University Port Harcourt, Rivers State, Nigeria.
L. Ebiwareme
Department of Mathematics, Rivers State University Port Harcourt, Rivers State, Nigeria.
O. I. Ekesiobi
Department of Mathematics, Rivers State University Port Harcourt, Rivers State, Nigeria.
P. E. Brown-Ikiri
Department of Mathematics, Rivers State University Port Harcourt, Rivers State, Nigeria.
F. Nnaa
Department of Mathematics, Rivers State University Port Harcourt, Rivers State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
New results for stability and feedback control of time delay systems were proposed. These results were obtained by using Lyapunov Razumikhin method to approximate the stability of the uncontrolled Volterra type system with delay and designing a state feedback controller using a model transformation technique, the Lyapunov matrix equation and the Razumikhin approach for the stabilization of the controlled Volterra type system with delay. Examples are given to illustrate the effectiveness of the theoretical results.
Keywords: Stability, lyapunov-razumikhin, controllability, delay system, feedback controller