메뉴 건너뛰기




Volumn 350, Issue 10, 2013, Pages 3365-3383

Maximal perturbation bounds for robust stabilizability of fractional-order systems with norm bounded perturbations

Author keywords

[No Author keywords available]

Indexed keywords

FRACTIONAL-ORDER SYSTEMS; LINEAR MATRIX INEQUALITY APPROACH; LINEAR MATRIX INEQUALITY SOLVER; LINEAR STATE FEEDBACK; NORM-BOUNDED PERTURBATION; PERTURBATION BOUNDS; ROBUST STABILIZABILITY; ROBUST STABILIZATION;

EID: 84887317918     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2013.07.014     Document Type: Article
Times cited : (15)

References (56)
  • 4
    • 51449107734 scopus 로고    scopus 로고
    • An introduction to the fractional continuous-time linear systems the 21st century systems
    • M.D. Ortigueira An introduction to the fractional continuous-time linear systems the 21st century systems IEEE Circuits and Systems Magazine 8 2008 19 26
    • (2008) IEEE Circuits and Systems Magazine , vol.8 , pp. 19-26
    • Ortigueira, M.D.1
  • 8
    • 78649591986 scopus 로고    scopus 로고
    • Fractional order circuits and systems an emerging interdiscplinary research area
    • A.S. Elwakil Fractional order circuits and systems an emerging interdiscplinary research area IEEE Circuits and Systems Magazine 10 2010 41 50
    • (2010) IEEE Circuits and Systems Magazine , vol.10 , pp. 41-50
    • Elwakil, A.S.1
  • 10
    • 85019485305 scopus 로고
    • The crone control of resonant plants application to a flexible transmission
    • A. Oustaloup, B. Mathieu, and P. Lanusse The crone control of resonant plants application to a flexible transmission European Journal of Control 1 1995 113 121
    • (1995) European Journal of Control , vol.1 , pp. 113-121
    • Oustaloup, A.1    Mathieu, B.2    Lanusse, P.3
  • 11
    • 36248973595 scopus 로고    scopus 로고
    • An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers
    • S.E. Hamamci An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers IEEE Transactions on Automatic Control 52 2007 1964 1969
    • (2007) IEEE Transactions on Automatic Control , vol.52 , pp. 1964-1969
    • Hamamci, S.E.1
  • 12
    • 38149057159 scopus 로고    scopus 로고
    • Optimal fractional controllers for rational order systems a special case of the Wiener-Hopf spectral factorization method
    • B.M. Vinagre, and V. Feliu Optimal fractional controllers for rational order systems a special case of the Wiener-Hopf spectral factorization method IEEE Transactions on Automatic Control 52 2007 2385 2389
    • (2007) IEEE Transactions on Automatic Control , vol.52 , pp. 2385-2389
    • Vinagre, B.M.1    Feliu, V.2
  • 13
    • 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
    • 84862794045 scopus 로고    scopus 로고
    • infin design with fractional-order PD controllers
    • infin design with fractional-order PD controllers Automatica 48 2012 974 977
    • (2012) Automatica , vol.48 , pp. 974-977
    • Wang, D.J.1    Gao, X.L.2
  • 15
    • 23144435914 scopus 로고    scopus 로고
    • A note on the fractional-order Chen system
    • J.G. Lu, and G.R. Chen A note on the fractional-order Chen system Chaos, Solitons and Fractals 27 2006 685 688
    • (2006) Chaos, Solitons and Fractals , vol.27 , pp. 685-688
    • Lu, J.G.1    Chen, G.R.2
  • 16
    • 78149363753 scopus 로고    scopus 로고
    • Field programmable analog array implementation of fractional step filters
    • T. Freeborn, B. Maundy, and A.S. Elwakil Field programmable analog array implementation of fractional step filters IET Circuits Devices and Systems 4 2010 514 524
    • (2010) IET Circuits Devices and Systems , vol.4 , pp. 514-524
    • Freeborn, T.1    Maundy, B.2    Elwakil, A.S.3
  • 18
    • 84862861613 scopus 로고    scopus 로고
    • High quality factor asymmetric-slope band-pass filters a fractional-order capacitor approach
    • P. Ahmadi, B. Maundy, A.S. Elwakil, and L. Belostotski High quality factor asymmetric-slope band-pass filters a fractional-order capacitor approach IET Circuits Devices and Systems 6 2012 141 210
    • (2012) IET Circuits Devices and Systems , vol.6 , pp. 141-210
    • Ahmadi, P.1    Maundy, B.2    Elwakil, A.S.3    Belostotski, L.4
  • 21
    • 0026124343 scopus 로고
    • Fractional-order state equations for the control of viscoelastic damped structures
    • R.L. Bagley, and R.A. Calico Fractional-order state equations for the control of viscoelastic damped structures Journal of Guidance, Control and Dynamics 14 1991 304 311
    • (1991) Journal of Guidance, Control and Dynamics , vol.14 , pp. 304-311
    • Bagley, R.L.1    Calico, R.A.2
  • 24
    • 80052465626 scopus 로고    scopus 로고
    • Unexpected results of extended fractional Kalman filter for parameter identification in fractional order chaotic systems
    • G.H. Sun, M. Wang, and L.G. Wu Unexpected results of extended fractional Kalman filter for parameter identification in fractional order chaotic systems International Journal of Innovative Computing, Information and Control 7 2011 5341 5352
    • (2011) International Journal of Innovative Computing, Information and Control , vol.7 , pp. 5341-5352
    • Sun, G.H.1    Wang, M.2    Wu, L.G.3
  • 25
    • 65549098895 scopus 로고    scopus 로고
    • On the stability of linear systems with fractional-order elements
    • A.G. Radwan, A.M. Soliman, and A.S. Elwakil On the stability of linear systems with fractional-order elements Chaos, Solitons and Fractals 40 2009 2317 2328
    • (2009) Chaos, Solitons and Fractals , vol.40 , pp. 2317-2328
    • Radwan, A.G.1    Soliman, A.M.2    Elwakil, A.S.3
  • 26
    • 84858841611 scopus 로고    scopus 로고
    • Stability analysis of Caputo fractional-order nonlinear systems revisited
    • H. Delavari, D. Baleanu, and J. Sadati Stability analysis of Caputo fractional-order nonlinear systems revisited Nonlinear Dynamics 67 2012 2433 2439
    • (2012) Nonlinear Dynamics , vol.67 , pp. 2433-2439
    • Delavari, H.1    Baleanu, D.2    Sadati, 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
  • 30
    • 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
  • 31
    • 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
  • 33
    • 61549083723 scopus 로고    scopus 로고
    • Robust stability analysis of fractional order interval polynomials
    • N. Tan, O.F. Özguven, and M.M. Özyetkin Robust stability analysis of fractional order interval polynomials ISA Transactions 48 2009 166 172
    • (2009) ISA Transactions , vol.48 , pp. 166-172
    • Tan, N.1    Özguven, O.F.2    Özyetkin, M.M.3
  • 34
    • 77956400175 scopus 로고    scopus 로고
    • Pseudo-state feedback stabilization of commensurate fractional order systems
    • C. Farges, M. Moze, and J. Sabatier Pseudo-state feedback stabilization of commensurate fractional order systems Automatica 46 2010 1730 1734
    • (2010) Automatica , vol.46 , pp. 1730-1734
    • Farges, C.1    Moze, M.2    Sabatier, J.3
  • 35
    • 84861714671 scopus 로고    scopus 로고
    • Fractional order polytopic systems robust stability and stabilisation
    • C. Farges, J. Sabatier, and M. Moze Fractional order polytopic systems robust stability and stabilisation Advances in Difference Equations 2011 2011 1 10
    • (2011) Advances in Difference Equations , vol.2011 , pp. 1-10
    • Farges, C.1    Sabatier, J.2    Moze, M.3
  • 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 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 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
    • 84864659687 scopus 로고    scopus 로고
    • Robust stability and stabilization of fractional order interval systems with coupling relationships the 0 < α < 1 case
    • C. Li, and J.C. Wang Robust stability and stabilization of fractional order interval systems with coupling relationships the 0 < α < 1 case Journal of the Franklin Institute 349 2012 2406 2419
    • (2012) Journal of the Franklin Institute , vol.349 , pp. 2406-2419
    • Li, C.1    Wang, J.C.2
  • 39
    • 79957607884 scopus 로고    scopus 로고
    • Robust stability analysis for a class of fractional order systems with uncertain parameters
    • Z. Liao, C. Peng, W. Li, and Y. Wang 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
    • Liao, Z.1    Peng, C.2    Li, W.3    Wang, Y.4
  • 40
    • 79960979680 scopus 로고    scopus 로고
    • LMI-based robust control of fractional-order uncertain linear systems
    • Y.H. Lan, and Y. Zhou LMI-based robust control of fractional-order uncertain linear systems Computers and Mathematics with Applications 62 2011 1460 1471
    • (2011) Computers and Mathematics with Applications , vol.62 , pp. 1460-1471
    • Lan, Y.H.1    Zhou, Y.2
  • 42
    • 80051510187 scopus 로고    scopus 로고
    • Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control
    • T.C. Lin, and T.Y. Lee Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control IEEE Transactions on Fuzzy Systems 19 2011 623 635
    • (2011) IEEE Transactions on Fuzzy Systems , vol.19 , pp. 623-635
    • Lin, T.C.1    Lee, T.Y.2
  • 43
    • 84856604260 scopus 로고    scopus 로고
    • Control of an uncertain fractional order economic system via adaptive sliding mode
    • Z. Wang, X. Huang, and H. Shen Control of an uncertain fractional order economic system via adaptive sliding mode Neurocomputing 83 2012 83 88
    • (2012) Neurocomputing , vol.83 , pp. 83-88
    • Wang, Z.1    Huang, X.2    Shen, H.3
  • 44
    • 84861726301 scopus 로고    scopus 로고
    • Finite-time chaos control and synchronization of fractional-order chaotic (hyperchaotic) systems via fractional nonsingular terminal sliding mode technique
    • M.P. Aghababa Finite-time chaos control and synchronization of fractional-order chaotic (hyperchaotic) systems via fractional nonsingular terminal sliding mode technique Nonlinear Dynamics 69 2012 247 261
    • (2012) Nonlinear Dynamics , vol.69 , pp. 247-261
    • Aghababa, M.P.1
  • 45
    • 84855222892 scopus 로고    scopus 로고
    • Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller
    • M.P. Aghababa Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller Communications in Nonlinear Science and Numerical Simulation 17 2012 2670 2681
    • (2012) Communications in Nonlinear Science and Numerical Simulation , vol.17 , pp. 2670-2681
    • Aghababa, M.P.1
  • 46
    • 84855813743 scopus 로고    scopus 로고
    • Robust finite-time stabilization of fractional-order chaotic systems based on fractional Lyapunov stability theory
    • M.P. Aghababa Robust finite-time stabilization of fractional-order chaotic systems based on fractional Lyapunov stability theory Journal of Computational and Nonlinear Dynamics 7 2012 021010-1 021010-5
    • (2012) Journal of Computational and Nonlinear Dynamics , vol.7 , pp. 0210101-0210105
    • Aghababa, M.P.1
  • 47
    • 84879783455 scopus 로고    scopus 로고
    • A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems
    • M.P. Aghababa, A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems, Nonlinear Dynamics 73 (2013) 679-688
    • (2013) Nonlinear Dynamics , vol.73 , pp. 679-688
    • Aghababa, M.P.1
  • 49
    • 0030108725 scopus 로고    scopus 로고
    • infin control of systems with parameter uncertainty
    • infin control of systems with parameter uncertainty International Journal of Control 63 1996 741 750
    • (1996) International Journal of Control , vol.63 , pp. 741-750
    • Xie, L.1
  • 53
    • 79953644724 scopus 로고    scopus 로고
    • Model approximation for discrete-time state-delay systems in the T-S fuzzy framework
    • L.G. Wu, X.J. Su, P. Shi, and J.B. Qiu Model approximation for discrete-time state-delay systems in the T-S fuzzy framework IEEE Transactions on Fuzzy Systems 19 2011 366 378
    • (2011) IEEE Transactions on Fuzzy Systems , vol.19 , pp. 366-378
    • Wu, L.G.1    Su, X.J.2    Shi, P.3    Qiu, J.B.4
  • 54
    • 84868191701 scopus 로고    scopus 로고
    • A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delay
    • X.J. Su, P. Shi, L.G. Wu, and Y.D. Song A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delay IEEE Transactions on Fuzzy Systems 20 2012 1114 1129
    • (2012) IEEE Transactions on Fuzzy Systems , vol.20 , pp. 1114-1129
    • Su, X.J.1    Shi, P.2    Wu, L.G.3    Song, Y.D.4
  • 56
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • K. Diethelm, N.J. Ford, and A.D. Freed A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dynamics 29 2002 3 22
    • (2002) Nonlinear Dynamics , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.