Necessary and sufficient stability condition of fractional-order interval linear systems
This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix A is an interval uncertain matrix and fractional commensurate order belongs to 1 ≤ α < 2 . Using the existence condition of Hermitian P = P ∗ fo...
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| Published in | Automatica (Oxford) Vol. 44; no. 11; pp. 2985 - 2988 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Ltd
01.11.2008
Elsevier |
| Subjects | |
| Online Access | Get full text |
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| Abstract | This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix
A
is an interval uncertain matrix and fractional commensurate order belongs to
1
≤
α
<
2
. Using the existence condition of Hermitian
P
=
P
∗
for a complex Lyapunov inequality, we prove that the fractional-order interval linear system is robust stable if and only if there exists Hermitian matrix
P
=
P
∗
such that a certain type of complex Lyapunov inequality is satisfied for all vertex matrices. The results are directly extended to the robust stability condition of fractional-order interval polynomial systems. |
|---|---|
| AbstractList | This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix
A
is an interval uncertain matrix and fractional commensurate order belongs to
1
≤
α
<
2
. Using the existence condition of Hermitian
P
=
P
∗
for a complex Lyapunov inequality, we prove that the fractional-order interval linear system is robust stable if and only if there exists Hermitian matrix
P
=
P
∗
such that a certain type of complex Lyapunov inequality is satisfied for all vertex matrices. The results are directly extended to the robust stability condition of fractional-order interval polynomial systems. |
| Author | Ahn, Hyo-Sung Chen, YangQuan |
| Author_xml | – sequence: 1 givenname: Hyo-Sung surname: Ahn fullname: Ahn, Hyo-Sung email: hyosung@gist.ac.kr organization: Department of Mechatronics, Gwangju Institute of Science and Technology (GIST), 1 Oryong-dong, Buk-gu, Gwangju 500-712, Republic of Korea – sequence: 2 givenname: YangQuan surname: Chen fullname: Chen, YangQuan email: yqchen@ece.usu.edu organization: Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical and Computer Engineering, 4160 Old Main Hill, Utah State University, Logan, UT 84322-4160, USA |
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| Cites_doi | 10.1016/j.amc.2006.08.099 10.3182/20080706-5-KR-1001.02580 10.1109/9.739144 10.1109/9.940935 10.1016/S0947-3580(95)70014-0 10.1016/S0165-1684(03)00181-6 |
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| Keywords | Interval uncertainty Necessary and sufficient stability condition Fractional-order linear systems Robust stability Necessary and sufficient condition Hermitian matrix Interval arithmetic Fractional derivative Robust control Uncertain system Polynomial interpolation Interval matrix Robustness Lyapunov function |
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| References_xml | – volume: 83 start-page: 2285 year: 2003 end-page: 2480 ident: b7 article-title: Special issue on fractional signal processing and applications publication-title: Signal Processing (Guest Editors) – reference: Chen, Y., Ahn, H. -S., & Podlubny, I. (2005). Robust stability check of fractional order linear time invariant systems with interval uncertainties. In – reference: (pp. 15256–15261) – volume: 80 start-page: 589 year: 1960 end-page: 597 ident: b1 article-title: The non-integer integral and its application to control systems publication-title: JIEE (Japanese Institute of Electrical Engineers) Journal – volume: 187 start-page: 27 year: 2007 end-page: 34 ident: b3 article-title: Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality publication-title: Applied Mathematics and Computation – volume: 1 year: 1995 ident: b8 article-title: The CRONE control of resonant plants: Application to a flexible transmission publication-title: European Journal of Control – volume: 46 start-page: 1285 year: 2001 end-page: 1288 ident: b6 article-title: Rank-one LMIs and Lyapunov’s inequality publication-title: IEEE Transactions on Automatic Control – volume: 44 start-page: 208 year: 1999 end-page: 214 ident: b9 article-title: Fractional-order systems and publication-title: IEEE Transactions on Automatic Control – reference: Ahn, H.-S., & Chen, Y. (2008). Conservatism-free robust stability check of fractional-order interval linear systems. In – volume: 6 start-page: 83 year: 1961 end-page: 87 ident: b2 article-title: The non-integer integral and its application to control systems publication-title: ETJ of Japan – reference: (pp. 210–215) – volume: 3 start-page: 393 year: 1975 end-page: 399 ident: b5 article-title: The stabilizing solution of the discrete algebraic Riccati equation publication-title: IEEE Transactions on Automatic Control – ident: 10.1016/j.automatica.2008.07.003_b4 – volume: 80 start-page: 589 issue: 860 year: 1960 ident: 10.1016/j.automatica.2008.07.003_b1 article-title: The non-integer integral and its application to control systems publication-title: JIEE (Japanese Institute of Electrical Engineers) Journal – volume: 187 start-page: 27 issue: 1 year: 2007 ident: 10.1016/j.automatica.2008.07.003_b3 article-title: Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2006.08.099 – ident: 10.1016/j.automatica.2008.07.003_b10 doi: 10.3182/20080706-5-KR-1001.02580 – volume: 3 start-page: 393 year: 1975 ident: 10.1016/j.automatica.2008.07.003_b5 article-title: The stabilizing solution of the discrete algebraic Riccati equation publication-title: IEEE Transactions on Automatic Control – volume: 44 start-page: 208 issue: 1 year: 1999 ident: 10.1016/j.automatica.2008.07.003_b9 article-title: Fractional-order systems and PIλDμ-controllers publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.739144 – volume: 46 start-page: 1285 issue: 8 year: 2001 ident: 10.1016/j.automatica.2008.07.003_b6 article-title: Rank-one LMIs and Lyapunov’s inequality publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.940935 – volume: 1 issue: 2 year: 1995 ident: 10.1016/j.automatica.2008.07.003_b8 article-title: The CRONE control of resonant plants: Application to a flexible transmission publication-title: European Journal of Control doi: 10.1016/S0947-3580(95)70014-0 – volume: 83 start-page: 2285 issue: 11 year: 2003 ident: 10.1016/j.automatica.2008.07.003_b7 article-title: Special issue on fractional signal processing and applications publication-title: Signal Processing (Guest Editors) doi: 10.1016/S0165-1684(03)00181-6 – volume: 6 start-page: 83 issue: 3–4 year: 1961 ident: 10.1016/j.automatica.2008.07.003_b2 article-title: The non-integer integral and its application to control systems publication-title: ETJ of Japan |
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| Snippet | This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix
A
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| SubjectTerms | Applied sciences Computer science; control theory; systems Control system analysis Control theory. Systems Exact sciences and technology Fractional-order linear systems Interval uncertainty Necessary and sufficient stability condition |
| Title | Necessary and sufficient stability condition of fractional-order interval linear systems |
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