A POLYNOMIAL METHOD FOR STABILITY ANALYSIS OF LTI SYSTEMS INDEPENDENT OF DELAYS.
Saved in:
| Title: | A POLYNOMIAL METHOD FOR STABILITY ANALYSIS OF LTI SYSTEMS INDEPENDENT OF DELAYS. |
|---|---|
| Authors: | ALIKOC, BARAN1 baran.alikoc@itu.edu.tr, ERGENC, ALI FUAT1 ali.ergenc@itu.edu.tr |
| Source: | SIAM Journal on Control & Optimization. 2017, Vol. 55 Issue 4, p2661-2683. 23p. |
| Subjects: | Polynomials, Sweeping & dusting, Mathematics, Algebra |
| Abstract: | A new method providing necessary and sufficient conditions to test delay-independent stability for general linear time-invariant systems with constant delays is proposed. The method is utilized for single delay and incommensurate multiple delay systems. The proposed method offers an approach to determine the exact boundaries of unknown parameters such as controller gains or system parameters ensuring delay-independent stability, in addition to exhibiting an efficient test for real parameters. The technique is based on nonexistence of unitary complex zeros of an auxiliary characteristic polynomial obtained via extended Kronecker summation. A special feature of the polynomial, i.e., the self-inversive property, is proved and utilized to check its unitary zeros to determine delay-independent stability by an efficient zero location test. The methodology is executed employing simple algebraic operations and inspection of the number of sign variations in the obtained sequence. For the single delay case, the procedure does not require parameter (or frequency) sweeping, equation solving, and pointwise testing even for the determination of the delayindependent stabilizing regions of unknown parameters. In the case of systems with p multiple delays, (p - 2) agent parameters in the range [0, 2π] and one agent parameter in the range [0, π] are swept to determine delay-independent stability without the requirement of solving equations. A graphical projection approach for multiple delays is proposed in the case in which unknown parameters exist. The complete delay-independent stability analysis of a second order PD-controlled system with single delay is presented. Moreover, the method is applied to find the exact delay-independent stabilizing regions of unknown parameters of systems with two and three delays. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Control & Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 126381735 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: A POLYNOMIAL METHOD FOR STABILITY ANALYSIS OF LTI SYSTEMS INDEPENDENT OF DELAYS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22ALIKOC%2C+BARAN%22">ALIKOC, BARAN</searchLink><relatesTo>1</relatesTo><i> baran.alikoc@itu.edu.tr</i><br /><searchLink fieldCode="AR" term="%22ERGENC%2C+ALI+FUAT%22">ERGENC, ALI FUAT</searchLink><relatesTo>1</relatesTo><i> ali.ergenc@itu.edu.tr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Control+%26+Optimization%22">SIAM Journal on Control & Optimization</searchLink>. 2017, Vol. 55 Issue 4, p2661-2683. 23p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Sweeping+%26+dusting%22">Sweeping & dusting</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A new method providing necessary and sufficient conditions to test delay-independent stability for general linear time-invariant systems with constant delays is proposed. The method is utilized for single delay and incommensurate multiple delay systems. The proposed method offers an approach to determine the exact boundaries of unknown parameters such as controller gains or system parameters ensuring delay-independent stability, in addition to exhibiting an efficient test for real parameters. The technique is based on nonexistence of unitary complex zeros of an auxiliary characteristic polynomial obtained via extended Kronecker summation. A special feature of the polynomial, i.e., the self-inversive property, is proved and utilized to check its unitary zeros to determine delay-independent stability by an efficient zero location test. The methodology is executed employing simple algebraic operations and inspection of the number of sign variations in the obtained sequence. For the single delay case, the procedure does not require parameter (or frequency) sweeping, equation solving, and pointwise testing even for the determination of the delayindependent stabilizing regions of unknown parameters. In the case of systems with p multiple delays, (p - 2) agent parameters in the range [0, 2π] and one agent parameter in the range [0, π] are swept to determine delay-independent stability without the requirement of solving equations. A graphical projection approach for multiple delays is proposed in the case in which unknown parameters exist. The complete delay-independent stability analysis of a second order PD-controlled system with single delay is presented. Moreover, the method is applied to find the exact delay-independent stabilizing regions of unknown parameters of systems with two and three delays. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Control & Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=126381735 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/16M1077726 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 2661 Subjects: – SubjectFull: Polynomials Type: general – SubjectFull: Sweeping & dusting Type: general – SubjectFull: Mathematics Type: general – SubjectFull: Algebra Type: general Titles: – TitleFull: A POLYNOMIAL METHOD FOR STABILITY ANALYSIS OF LTI SYSTEMS INDEPENDENT OF DELAYS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: ALIKOC, BARAN – PersonEntity: Name: NameFull: ERGENC, ALI FUAT IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: 2017 Type: published Y: 2017 Identifiers: – Type: issn-print Value: 03630129 Numbering: – Type: volume Value: 55 – Type: issue Value: 4 Titles: – TitleFull: SIAM Journal on Control & Optimization Type: main |
| ResultId | 1 |
