Open Access
2017 New Conditions for the Exponential Stability of Nonlinear Differential Equations
Rigoberto Medina
Abstr. Appl. Anal. 2017: 1-7 (2017). DOI: 10.1155/2017/4640835


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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Rigoberto Medina. "New Conditions for the Exponential Stability of Nonlinear Differential Equations." Abstr. Appl. Anal. 2017 1 - 7, 2017.


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

zbMATH: 06929557
MathSciNet: MR3638980
Digital Object Identifier: 10.1155/2017/4640835

Rights: Copyright © 2017 Hindawi

Vol.2017 • 2017
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