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On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems
-
Shota Akhalaia
Published/Copyright:
March 11, 2010
Abstract
Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations
𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡),
where 
and 
are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from 
. The results are realized for the linear systems of impulsive, ordinary differential and difference equations.
Key words and phrases:: Stability in the Lyapunov sense; linear system of generalized ordinary differential equations; Lebesgue–Stiltjes integral; linear system of impulsive equations; linear system of ordinary differential equations; linear system of difference equations
Received: 2008-05-16
Published Online: 2010-03-11
Published in Print: 2009-December
© Heldermann Verlag
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Articles in the same Issue
- On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems
- Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations
- Unilateral Contact Problems with Friction for Hemitropic Elastic Solids
- A Periodic Boundary Value Problem for Functional Differential Equations of Higher Order
- The Jawerth–Franke Embedding of Spaces with Dominating Mixed Smoothness
- Stability by Fixed Point Theory for Nonlinear Delay Difference Equations
- On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their Bézier Variant
- On Nonmeasurable Functions of Two Variables and Iterated Integrals
- Bounded and Vanishing at Infinity Solutions of Nonlinear Differential Systems
- On Functional Equations Connected with Quadrature Rules
- The Riemann–Hilbert Problem in a Domain with Piecewise Smooth Boundaries in Weight Classes of Cauchy Type Integrals with a Density from Variable Exponent Lebesgue Spaces
- A Counterexample on Embedding of Spaces
- On Solutions of a Singular Viscoelastic Equation with an Integral Condition
- Nonbounding 𝑛-C.E. 𝑄-Degrees
- Nonequivalence of Unilateral Strong Differentiation Bases in
