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undergraduate thesis
Stabilizabilnost LT sustava
2020. urn:nbn:hr:126:187298
Šokčević, Dražen
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Geometry and Mathematics Teaching Mathematics Research Group

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Šokčević, D. (2020). Stabilizabilnost LT sustava (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:187298

Šokčević, Dražen. "Stabilizabilnost LT sustava." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:187298

Šokčević, Dražen. "Stabilizabilnost LT sustava." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:187298

Šokčević, D. (2020). 'Stabilizabilnost LT sustava', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 23 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:187298

Šokčević D. Stabilizabilnost LT sustava [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2025 January 23] Available at: https://urn.nsk.hr/urn:nbn:hr:126:187298

D. Šokčević, "Stabilizabilnost LT sustava", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:187298

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Metadata
TitleStabilizabilnost LT sustava
Title (english)Stabilizability at LT System
AuthorDražen Šokčević
MentorZoran Tomljanović (mentor)
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 country2020-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom završnom radu bavimo se temom stabilizabilosti linearnih vremenski invarijantnih sustava. U početku rada definirat ćemo linearan vremenski invarijantan sustav te dokazati teorem za rješenje sustava. Definirat ćemo matričnu eksponencijalnu funkciju i navesti neka njezina svojstva koja se koriste za rješenje sustava. Obradit ćemo svojstva stabilnosti i upravljivosti sustava i dokazati teoreme koji se koriste za njihovu provjeru te ih na primjerima demonstrirati. Definirat ćemo pojam stabilizabilnosti sustava i povezati ga sa svojstvima stabilnosti i upravljivosti. Modelirat ćemo sustav koji opisuje dvostruko obrnuto njihalo na kolicima. Navedeni sustav ćemo stabilizirati na dva pristupa: koristeći Ackermannovu formulu te Ljapunovljevu jednadžbu, a usporedbu stabilizacije ćemo ilustrirati na numeričkom primjeru.
Abstract (english)
In this final paper we deal with the subject of stabilizability of linear time invariant systems. At the beginning of the paper, we will define a linear time invariant system and prove a theorem for the solution of the system. We will define a matrix exponential function and list some of its properties that are used to solve the system. We will study the properties of stability and controllability for linear time invariant system and prove the theorems used to check them. Considered properties will be illustrated on examples. Furthermore we will define stabilizability for system and relate it to the properties of stability and controllability. We will model a system describing a double inverted pendulum mounted on a cart. This system will be stabilized with two approaches: using Ackermann’s formula and Lyapunov equation. On numerical example we will illustrate comparison of these two stabilization approaches.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:187298
Study programmeTitle: Bachelor of Mathematics and Computer Science
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-10-30 07:01:31