Geodesic
Exponential stability of nonlinear non-autonomous multivariable systems
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 35 (2015) no. 1, pp. 89-100.

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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.
Keywords: nonlinear nonautonomous systems, exponential stability, absolute stability 
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Gil', Michael. Exponential stability of nonlinear non-autonomous multivariable systems. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 35 (2015) no. 1, pp. 89-100. http://geodesic.mathdoc.fr/item/DMDICO_2015_35_1_a4/

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