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**Lyapunov stability of systems of linear generalized ordinary differential equations.**
*(English)*
Zbl 1090.34043

Summary: Effective necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of the linear system of generalized ordinary differential equations
\[
dx(t)=dA(t)\cdot x(t)+df(t),
\]
where \(A:\mathbb{R}_+\to \mathbb{R}^{n\times n}\) and \(f:\mathbb{R}_+\to\mathbb{R}^n\) \((\mathbb{R}_+[0,+\infty[)\) are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from \(\mathbb{R}_+\), having properties analogous to the case of systems of ordinary differential equations with constant coefficients. The results obtained are realized for linear systems of both impulsive equations and difference equations.

### MSC:

34D20 | Stability of solutions to ordinary differential equations |

34A30 | Linear ordinary differential equations and systems |

34A37 | Ordinary differential equations with impulses |

39A12 | Discrete version of topics in analysis |

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\textit{M. Ashordia}, Comput. Math. Appl. 50, No. 5--6, 957--982 (2005; Zbl 1090.34043)

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### References:

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