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.
Highlights
The presence of time delay in mathematical model equations has helped in making the system equations more realistic
A retarded differential equation is a functional differential equation with delay incorporated only in the state of the system, which accounts for the past state of the system (Asl and Ulsoy, 2003)
A general retarded differential equation is of the form, x&(t) = f (t,x(t), x(t −nh)), n=1,2,3,.,
Summary
The presence of time delay in mathematical model equations has helped in making the system equations more realistic. Utilized the linear matrix inequality properties of the system matrix equation, and proved that it satisfies the Lyapunov – Krasovskii conditions for asymptotic stability.
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