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Abstract
Necessary and sufficient conditions and effective sufficient conditions are established for the so-called ξ-exponentially asymptotic stability of the linear system
𝑑𝑥(𝑡) = 𝑑𝘈(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡),
where and are respectively matrix- and vector-functions with bounded variation components, on every closed interval from [0, +∞[ and ξ : [0, +∞[ → [0, +∞[ is a nondecreasing function such that .
Key words and phrases:: ξ-exponentially asymptotic stablility in the Lyapunov sense; linear generalized ordinary differential equations; Lebesgue–Stiltjes integral
Received: 2001-03-13
Published Online: 2010-02-25
Published in Print: 2001-December
© Heldermann Verlag