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On the \(\xi\)-exponentially asymptotic stability of linear systems of generalized ordinary differential equations. (English) Zbl 1014.34038
Summary: Necessary and sufficient conditions and effective sufficient conditions are established for the so-called \(\xi\)-exponentially asymptotic stability of the linear system \[ dx(t)=DA(t)\cdot x(t)+df(t), \] where \(A:[0,+\infty [\to\mathbb{R}^{n\times n}\) and \(f:[0,+\infty [\to\mathbb{R}^n\) are, respectively, matrix and vector functions with bounded variation components on every closed interval from \([0,+\infty[\) and \(\xi:[0,+\infty [\to[0,+\infty[\) is a nondecreasing function such that \(\lim_{t\to+ \infty}\xi(t)= +\infty\).

MSC:
34D20 Stability of solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems
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