메뉴 건너뛰기




Volumn 349, Issue 7, 2012, Pages 2406-2419

Robust stability and stabilization of fractional order interval systems with coupling relationships: The 0<α<1 case

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTICAL STABILITY; FRACTIONAL ORDER; INPUT MATRICES; INTERVAL SYSTEMS; LINEAR COUPLING; LINEAR TIME INVARIANT; NUMERICAL EXAMPLE; ROBUST STABILITY; STABILIZING CONTROLLERS; SUFFICIENT CONDITIONS; SYSTEM MATRICES;

EID: 84864659687     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2012.05.006     Document Type: Article
Times cited : (66)

References (40)
  • 3
    • 41349117569 scopus 로고    scopus 로고
    • Fractional Langevin model of memory in financial markets
    • 046118
    • S. Picozzi, and B.J. West Fractional Langevin model of memory in financial markets Physical Review E 66 046118 2002 1 12
    • (2002) Physical Review e , vol.66 , pp. 1-12
    • Picozzi, S.1    West, B.J.2
  • 7
    • 73649084378 scopus 로고    scopus 로고
    • On the passive control of vibrations with viscoelastic dynamic absorbers of ordinary and pendulum types
    • J.J. de Espíndola, C.A. Bavastri, and E.M.O. Lopes On the passive control of vibrations with viscoelastic dynamic absorbers of ordinary and pendulum types Journal of the Franklin Institute 347 2010 102 115
    • (2010) Journal of the Franklin Institute , vol.347 , pp. 102-115
    • De Espíndola, J.J.1    Bavastri, C.A.2    Lopes, E.M.O.3
  • 8
    • 0032653954 scopus 로고    scopus 로고
    • Fractional-order systems and PI (lambda) D (mu)-controllers
    • I. Podlubny Fractional-order systems and PI (lambda) D (mu)-controllers IEEE Transactions on Automatic Control 44 1999 208 214
    • (1999) IEEE Transactions on Automatic Control , vol.44 , pp. 208-214
    • Podlubny, I.1
  • 9
    • 0242270972 scopus 로고    scopus 로고
    • Two direct Tustin discretization methods for fractional-order differentiator/integrator
    • B.M. Vinagre, Y.Q. Chen, and I. Petras Two direct Tustin discretization methods for fractional-order differentiator/integrator Journal of the Franklin Institute 340 2003 349 362
    • (2003) Journal of the Franklin Institute , vol.340 , pp. 349-362
    • Vinagre, B.M.1    Chen, Y.Q.2    Petras, I.3
  • 10
    • 79251595176 scopus 로고    scopus 로고
    • Application of numerical inverse Laplace transform algorithms in fractional calculus
    • 315-330
    • H. Sheng, Y. Li, and Y.Q. Chen Application of numerical inverse Laplace transform algorithms in fractional calculus Journal of the Franklin Institute 2011 315-330
    • (2011) Journal of the Franklin Institute
    • Sheng, H.1    Li, Y.2    Chen, Y.Q.3
  • 11
    • 70049104872 scopus 로고    scopus 로고
    • Fractional order [proportional derivative] controller for a class of fractional order systems
    • Y. Luo, and Y.Q. Chen Fractional order [proportional derivative] controller for a class of fractional order systems Automatica 45 2009 2446 2450
    • (2009) Automatica , vol.45 , pp. 2446-2450
    • Luo, Y.1    Chen, Y.Q.2
  • 14
    • 80054903851 scopus 로고    scopus 로고
    • A note on phase synchronization in coupled chaotic fractional order systems
    • Z. Odibat A note on phase synchronization in coupled chaotic fractional order systems Nonlinear Analysis: Real World Applications 13 2011 779 789
    • (2011) Nonlinear Analysis: Real World Applications , vol.13 , pp. 779-789
    • Odibat, Z.1
  • 15
    • 41849090145 scopus 로고    scopus 로고
    • Chaos in the fractional order unified system and its synchronization
    • X. Wu, J. Li, and G. Chen Chaos in the fractional order unified system and its synchronization Journal of the Franklin Institute 345 2008 392 401
    • (2008) Journal of the Franklin Institute , vol.345 , pp. 392-401
    • Wu, X.1    Li, J.2    Chen, G.3
  • 16
    • 77958015559 scopus 로고    scopus 로고
    • Generalized lag-synchronization of chaotic mix-delayed systems with uncertain parameters and unknown perturbations
    • X. Yang, Q. Zhu, and C. Huang Generalized lag-synchronization of chaotic mix-delayed systems with uncertain parameters and unknown perturbations Nonlinear Analysis: Real World Applications 12 2011 93 105
    • (2011) Nonlinear Analysis: Real World Applications , vol.12 , pp. 93-105
    • Yang, X.1    Zhu, Q.2    Huang, C.3
  • 17
    • 80255123859 scopus 로고    scopus 로고
    • Chaotic synchronization between different fractional-order chaotic systems
    • P. Zhou, and R. Ding Chaotic synchronization between different fractional-order chaotic systems Journal of the Franklin Institute 348 2011 2839 2848
    • (2011) Journal of the Franklin Institute , vol.348 , pp. 2839-2848
    • Zhou, P.1    Ding, R.2
  • 19
    • 78049342917 scopus 로고    scopus 로고
    • Initial conditions and initialization of linear fractional differential equations
    • J. Trigeassou, and N. Maamri Initial conditions and initialization of linear fractional differential equations Signal Processing 91 2011 427 436
    • (2011) Signal Processing , vol.91 , pp. 427-436
    • Trigeassou, J.1    Maamri, N.2
  • 21
    • 52349114093 scopus 로고    scopus 로고
    • Analog fractional order controller in temperature and motor control applications
    • G.W. Bohannan Analog fractional order controller in temperature and motor control applications Journal of Vibration and Control 14 2008 1487 1498
    • (2008) Journal of Vibration and Control , vol.14 , pp. 1487-1498
    • Bohannan, G.W.1
  • 24
    • 0002731965 scopus 로고    scopus 로고
    • Stability results for fractional differential equations with applications to control processing
    • D. Matignon, Stability results for fractional differential equations with applications to control processing, in: Proceedings of the Computational Engineering in Systems Applications, 1996, pp. 963-968.
    • (1996) Proceedings of the Computational Engineering in Systems Applications , pp. 963-968
    • Matignon, D.1
  • 25
    • 33947133956 scopus 로고    scopus 로고
    • Stability analysis of linear fractional differential system with multiple time delays
    • W. Deng, C. Li, and J. Li Stability analysis of linear fractional differential system with multiple time delays Nonlinear dynamics 48 2007 409 416
    • (2007) Nonlinear Dynamics , vol.48 , pp. 409-416
    • Deng, W.1    Li, C.2    Li, J.3
  • 27
    • 67649626081 scopus 로고    scopus 로고
    • Mittag-leffler stability of fractional order nonlinear dynamic systems
    • Y. Li, Y.Q. Chen, and I. Podlubny Mittag-leffler stability of fractional order nonlinear dynamic systems Automatica 45 2009 1965 1969
    • (2009) Automatica , vol.45 , pp. 1965-1969
    • Li, Y.1    Chen, Y.Q.2    Podlubny, I.3
  • 28
    • 76449092011 scopus 로고    scopus 로고
    • Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability
    • Y. Li, Y.Q. Chen, and I. Podlubny Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability Computers & Mathematics with Applications 59 2010 1810 1821
    • (2010) Computers & Mathematics with Applications , vol.59 , pp. 1810-1821
    • Li, Y.1    Chen, Y.Q.2    Podlubny, I.3
  • 29
    • 74149085532 scopus 로고    scopus 로고
    • On robust stability of LTI fractional-order delay systems of retarded and neutral type
    • K. Akbari Moornani, and M. Haeri On robust stability of LTI fractional-order delay systems of retarded and neutral type Automatica 46 2010 362 368
    • (2010) Automatica , vol.46 , pp. 362-368
    • Akbari Moornani, K.1    Haeri, M.2
  • 30
    • 80051682888 scopus 로고    scopus 로고
    • Stability analysis of fractional-order systems with double noncommensurate orders for matrix case
    • Z. Jiao, and Y.Q. Chen Stability analysis of fractional-order systems with double noncommensurate orders for matrix case Fractional Calculus and Applied Analysis 14 2011 436 453
    • (2011) Fractional Calculus and Applied Analysis , vol.14 , pp. 436-453
    • Jiao, Z.1    Chen, Y.Q.2
  • 32
    • 33745872964 scopus 로고    scopus 로고
    • Robust stability check of fractional order linear time invariant systems with interval uncertainties
    • Y.Q. Chen, H.S. Ahn, and I. Podlubny Robust stability check of fractional order linear time invariant systems with interval uncertainties Signal Processing 86 2006 2611 2618
    • (2006) Signal Processing , vol.86 , pp. 2611-2618
    • Chen, Y.Q.1    Ahn, H.S.2    Podlubny, I.3
  • 33
    • 34247502196 scopus 로고    scopus 로고
    • Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality
    • H.S. Ahn, Y.Q. Chen, and I. Podlubny Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality Applied Mathematics and Computation 187 2007 27 34
    • (2007) Applied Mathematics and Computation , vol.187 , pp. 27-34
    • Ahn, H.S.1    Chen, Y.Q.2    Podlubny, I.3
  • 34
    • 79961018552 scopus 로고    scopus 로고
    • Conservatism-free robust stability check of fractional-order interval linear systems
    • H.S. Ahn, Y.Q. Chen, Conservatism-free robust stability check of fractional-order interval linear systems, in: Proceedings of the 17th IFAC world congress, 2008, pp. 15256-15261.
    • (2008) Proceedings of the 17th IFAC World Congress , pp. 15256-15261
    • Ahn, H.S.1    Chen, Y.Q.2
  • 35
    • 55249087154 scopus 로고    scopus 로고
    • Necessary and sufficient stability condition of fractional-order interval linear systems
    • H.S. Ahn, and Y.Q. Chen Necessary and sufficient stability condition of fractional-order interval linear systems Automatica 44 2008 2985 2988
    • (2008) Automatica , vol.44 , pp. 2985-2988
    • Ahn, H.S.1    Chen, Y.Q.2
  • 36
    • 67649619829 scopus 로고    scopus 로고
    • Robust stability and stabilization of fractional-order interval systems: An LMI approach
    • J.G. LU, and G.R. Chen Robust stability and stabilization of fractional-order interval systems: an LMI approach IEEE Transactions on Automatic Control 54 2009 1294 1299
    • (2009) IEEE Transactions on Automatic Control , vol.54 , pp. 1294-1299
    • Lu, J.G.1    Chen, G.R.2
  • 37
    • 75449099727 scopus 로고    scopus 로고
    • Robust stability and stabilization of fractional-order interval systems with the fractional order alpha: The 0<α<1 case
    • J.G. LU, and Y.Q. Chen Robust stability and stabilization of fractional-order interval systems with the fractional order alpha: the 0<α<1 case IEEE Transactions on Automatic Control 55 2010 152. 158
    • (2010) IEEE Transactions on Automatic Control , vol.55 , pp. 152-158
    • Lu, J.G.1    Chen, Y.Q.2
  • 38
    • 77955325027 scopus 로고    scopus 로고
    • Robust stabilization of fractional-order systems with interval uncertainties via fractional-order controllers
    • S.D. Saleh, A. MohammadMostafa, and H.B. Mohammadtaghi Robust stabilization of fractional-order systems with interval uncertainties via fractional-order controllers Advances in Difference Equations 2010 2010 1 15
    • (2010) Advances in Difference Equations , vol.2010 , pp. 1-15
    • Saleh, S.D.1    Mohammadmostafa, A.2    Mohammadtaghi, H.B.3
  • 39
    • 79957607884 scopus 로고    scopus 로고
    • Robust stability analysis for a class of fractional order systems with uncertain parameters
    • L. Zeng, P. Cheng, L. Wang, and W. Yong Robust stability analysis for a class of fractional order systems with uncertain parameters Journal of the Franklin Institute 348 2011 1101 1113
    • (2011) Journal of the Franklin Institute , vol.348 , pp. 1101-1113
    • Zeng, L.1    Cheng, P.2    Wang, L.3    Yong, W.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.