Abstract and Applied Analysis

New Conditions for the Exponential Stability of Nonlinear Differential Equations

Rigoberto Medina

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We develop a method for proving local exponential stability of nonlinear nonautonomous differential equations as well as pseudo-linear differential systems. The logarithmic norm technique combined with the “freezing” method is used to study stability of differential systems with slowly varying coefficients and nonlinear perturbations. Testable conditions for local exponential stability of pseudo-linear differential systems are given. Besides, we establish the robustness of the exponential stability in finite-dimensional spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. We illustrate the application of this test to linear approximations of the differential systems under consideration.

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Abstr. Appl. Anal., Volume 2017 (2017), Article ID 4640835, 7 pages.

Received: 23 January 2017
Accepted: 23 March 2017
First available in Project Euclid: 11 May 2017

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Medina, Rigoberto. New Conditions for the Exponential Stability of Nonlinear Differential Equations. Abstr. Appl. Anal. 2017 (2017), Article ID 4640835, 7 pages. doi:10.1155/2017/4640835. https://projecteuclid.org/euclid.aaa/1494468086

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