Asymptotic Stability Results of Solutions of Neutral Delay Systems

Abstract

In recent time, the delay equations have been widely used in the modeling of dynamic systems, most especially the neutral delay equations. But its asymptotic stability analysis proves to be more difficult. In this paper, a retarded delay system is transformed to a class of neutral delay system using the differentiability condition of the functional on the Banach space. The Leibnez-Newton formula and symmetric properties of some chosen matrices are utilized to formulate a Lyapunov functional of the transformed system, which satisfies the Lyapunov-Krasvoskii conditions for asymptotic stability. The computation of the maximum time-lag (h_m) for the system to attain stability is approximated by the difference integral equation of the integrodifferential equation. Numerical illustration confirms the suitability of the result.

Keywords: asymptotic stability, time delay, difference integral, integrodifferential equation, positive definite matrix

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 77 – 84