Asymptotic stability results for retarded differential systems

  • D.K Igobi
  • M.O Egwurube
  • M.R Odekunle
Keywords: Asymptotic stability, positive symmetric matrix, convex set segment, integral- differential equation.

Abstract

The transcendental character of the polynomial equation of the retarded differential system makes it difficult to express its solution explicitly. This has cause a set back in the asymptotic stability analysis of the system solutions. Various acceptable mathematical techniques have been used to address the issue. In this paper, the integral-differential equation and the positive symmetric properties of given matrices are used in formulating a Lyapunov functional. The introduction of convex set segment of a symmetric matrix is explored to establish boundedness of the first derivative of the formulated functional. The integral-differential equation is utilized in computing the maximum delay interval for the system to attain stability. Its application to numerical problems confirms the suitability of the test.
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eISSN: 1596-6208