Abstract
In this work various methods of Lyapunov quantities computation are discussed and implementations of symbolic computation algorithms, based on them, in Matlab are shown.
Highlights
Ðàçâèòèå ìåòîäîâ âû÷èñëåíèÿ è àíàëèçà ëÿïóíîâñêèõ âåëè÷èí ñòèìóëèðîâàëîñü êàê ÷èñòî ìàòåìàòè÷åñêèìè ïðîáëåìàìè (16-ÿ ïðîáëåìà Ãèëüáåðòà, çàäà÷à ðàçëè÷åíèÿ öåíòðà è ôîêóñà, îïðåäåëåíèå öèêëè÷íîñòè ôîêóñà, àíàëèç óñòîé÷èâîñòè äèíàìè÷åñêèõ ñèñòåì), òàê è ïðèêëàäíûìè èíæåíåðíûìè çàäà÷àìè
This begins possible by the development of analytical methods
This article describes various methods for computing Lyapunov quantities, and their computer implementation
Summary
Ñîâðåìåííûå ìåòîäû ñèìâîëüíûõ âû÷èñëåíèé: ëÿïóíîâñêèå âåëè÷èíû è 16-ÿ ïðîáëåìà Ãèëüáåðòà. Ëåîíîâ Ã.À., Êóçíåöîâ Í.Â., Êóäðÿøîâà Å.Â., Êóçíåöîâà Î.À. Äàííàÿ ðàáîòà ïîñâÿùåíà ðàçëè÷íûì ìåòîäàì âû÷èñëåíèÿ ëÿïóíîâñêèõ âåëè÷èí è ðåàëèçàöèÿì îñíîâàííûõ íà íèõ àëãîðèòìîâ ñèìâîëüíûõ âû÷èñëåíèé â ïàêåòå Ìàòëàá. Êëþ÷åâûå ñëîâà: ñèìâîëüíûå âû÷èñëåíèÿ, ëÿïóíîâñêèå âåëè÷èíû, ñëàáûé ôîêóñ, 16-ÿ ïðîáëåìà Ãèëüáåðòà, ìàëûå ïðåäåëüíûå öèêëû. Modern symbolic computation methods: Lyapunov quantities and 16th Hilbert problem
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