On solving the problems of stability by Lyapunov's direct method (Q682310)
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scientific article; zbMATH DE number 6838153
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On solving the problems of stability by Lyapunov's direct method |
scientific article; zbMATH DE number 6838153 |
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On solving the problems of stability by Lyapunov's direct method (English)
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14 February 2018
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In this paper, the author considers the system of non-autonomous differential equations \[ \dot x=f(x,t),\quad f(0,t)\equiv 0 \] defined in a neighborhood \(D\) of the origin of \(\mathbb R^n\). Conditions for stabilty, uniform stability, and instability of the zero solution of this system are obtained by means of theorems of Lyapunov's direct method with the use of semi-definite auxiliary functions. The results has been illustrated by examples, where a comparison with known results has been given.
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system of differential equations
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equilibrium
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stability
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Lyapunov's function
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0.94694316
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0.9361999
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