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ArticleOriginal scientific text

Title

Exponential stability of nonlinear non-autonomous multivariable systems

Authors 1

Affiliations

  1. Department of Mathematics, Ben Gurion University of the Negev, P.0. Box 653, Beer-Sheva 84105, Israel

Abstract

We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are formulated in terms of the norms of the derivatives and eigenvalues of the variable matrices, and certain scalar functions characterizing the nonlinearity. Moreover, an estimate for the solutions is derived. It gives us a bound for the region of attraction of the steady state. As a particular case we obtain absolute stability conditions. Our approach is based on a combined usage of the properties of the "frozen" Lyapunov equation, and recent norm estimates for matrix functions. An illustrative example is given.

Keywords

ENG
nonlinear nonautonomous systems, exponential stability, absolute stability

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2015/35/1
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Pages:
89-100
Main language of publication
English
Received
2015-06-03
Published
2015

DOI: 10.7151/dmdico.1168

Exact and natural sciences