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master's thesis
Stabilnost linearnih vremenski invarijantnih sustava
2021. urn:nbn:hr:126:679986
Borozan, Bartol
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Geometry and Mathematics Teaching Mathematics Research Group

Cite this document

Borozan, B. (2021). Stabilnost linearnih vremenski invarijantnih sustava (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:679986

Borozan, Bartol. "Stabilnost linearnih vremenski invarijantnih sustava." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:679986

Borozan, Bartol. "Stabilnost linearnih vremenski invarijantnih sustava." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:679986

Borozan, B. (2021). 'Stabilnost linearnih vremenski invarijantnih sustava', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 21 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:679986

Borozan B. Stabilnost linearnih vremenski invarijantnih sustava [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2025 January 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:679986

B. Borozan, "Stabilnost linearnih vremenski invarijantnih sustava", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:679986

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Metadata
TitleStabilnost linearnih vremenski invarijantnih sustava
Title (english)Stability of Linear Time Invariant systems
AuthorBartol Borozan
MentorZoran Tomljanović (mentor)
Committee memberKristian Sabo (predsjednik povjerenstva)
Committee memberZoran Tomljanović (član povjerenstva)
Committee memberDomagoj Matijević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Geometry and Mathematics Teaching Mathematics Research Group)
Osijek
Defense date and country2021-03-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Applied Mathematics and Mathematical Modeling
Abstract
Pojam stabilnosti je jedan od važnijih pojmova primijenjene matematike bitan mnogim znanstvenim disciplinama. Posebno je bitan u fizici i inženjerstvu gdje je proučavanje stabilnosti dovelo do novih saznanja. U ovome radu definiramo osnovne pojmove i navodimo rezultate vezane uz stabilnost linearnih vremenski invarijantnih sustava diferencijalnih jednadžbi. Preciznije, opisujemo stabilnost rješenja sustava u okolini točaka ravnoteže. Ovaj tip stabilnosti je poznat pod nazivom Ljapunovljeva stabilnost. Također definiramo i udaljenost do nestabilnog sustava i uvodimo algoritam koji će ju računati. Konačno, taj algoritam isprobavamo na nekoliko primjera te mjerimo njegovo vrijeme izvršavanja. Budući da se algoritam bazira na rješavanju svojstvenog problema, njegovo vrijeme izvršavanja se jako povećava s povećanjem dimenzije sustava.
Abstract (english)
Stability is an important concept in applied mathematics used in various scientific disciplines. It is particularly important in physics and engineering where its studying has led to new knowledge. In this paper we define basic concepts and show various results concerning stability of linear timeinvariant systems. More precisely, we study the stability of solutions of differential equations around equilibrium points. This type of stability is also known as Lyapunov stability. Furthermore, we define the distance to an unstable system and describe an algorithm to calculate it approximately. The algorithm is then tested and its running time captured on several examples. Since the algorithm is based on solving the eigenvalue problem, the running time rapidly increases with the size of input.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:679986
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-03-25 07:56:07