Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems
Based on the eigenvalue idea and the time-varying weighted vector norm in the state space <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="double-struck">R</mi> <mi>n</mi> </msup> </semantics>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/6/915 |
| _version_ | 1797566147157032960 |
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| author | Robert Vrabel |
| author_facet | Robert Vrabel |
| author_sort | Robert Vrabel |
| collection | DOAJ |
| description | Based on the eigenvalue idea and the time-varying weighted vector norm in the state space <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="double-struck">R</mi> <mi>n</mi> </msup> </semantics> </math> </inline-formula> we construct here the lower and upper bounds of the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the linear time-invariant systems to the linear time-varying ones. |
| first_indexed | 2024-03-10T19:22:33Z |
| format | Article |
| id | doaj.art-275c4170990e4d978294590454eae1ff |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T19:22:33Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-275c4170990e4d978294590454eae1ff2023-11-20T02:51:23ZengMDPI AGMathematics2227-73902020-06-018691510.3390/math8060915Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear SystemsRobert Vrabel0Institute of Applied Informatics, Automation and Mechatronics, Slovak University of Technology in Bratislava, Bottova 25, 917 01 Trnava, SlovakiaBased on the eigenvalue idea and the time-varying weighted vector norm in the state space <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="double-struck">R</mi> <mi>n</mi> </msup> </semantics> </math> </inline-formula> we construct here the lower and upper bounds of the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the linear time-invariant systems to the linear time-varying ones.https://www.mdpi.com/2227-7390/8/6/915linear time-varying systemuniformly asymptotically stable systemlower and upper bound on the solutionstime-varying vector normsimulation |
| spellingShingle | Robert Vrabel Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems Mathematics linear time-varying system uniformly asymptotically stable system lower and upper bound on the solutions time-varying vector norm simulation |
| title | Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems |
| title_full | Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems |
| title_fullStr | Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems |
| title_full_unstemmed | Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems |
| title_short | Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems |
| title_sort | time varying vector norm and lower and upper bounds on the solutions of uniformly asymptotically stable linear systems |
| topic | linear time-varying system uniformly asymptotically stable system lower and upper bound on the solutions time-varying vector norm simulation |
| url | https://www.mdpi.com/2227-7390/8/6/915 |
| work_keys_str_mv | AT robertvrabel timevaryingvectornormandlowerandupperboundsonthesolutionsofuniformlyasymptoticallystablelinearsystems |