메뉴 건너뛰기




Volumn 61, Issue 2, 2013, Pages 353-361

Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for the asymptotic stability

Author keywords

Cauchy's argument principle; discrete time fractional order systems; Gr nwald Letnikov fractional difference; stability conditions

Indexed keywords

ARGUMENT PRINCIPLES; CLOSED LOOP STABILITY; FRACTIONAL-ORDER SYSTEMS; NECESSARY AND SUFFICIENT STABILITY CONDITIONS; NUMERICAL PROCEDURES; STABILITY ANALYSIS; STABILITY CONDITION; STATE SPACE SYSTEMS;

EID: 84883470466     PISSN: 02397528     EISSN: None     Source Type: Journal    
DOI: 10.2478/bpasts-2013-0034     Document Type: Article
Times cited : (84)

References (39)
  • 2
    • 3042567794 scopus 로고    scopus 로고
    • Practical application of digital fractional-order controller to temperature control
    • I. Petráš and B. Vinagre, "Practical application of digital fractional-order controller to temperature control", Acta Montanistica Slovaca 7 (2), 131-137 (2002
    • (2002) Acta Montanistica Slovaca , vol.7 , Issue.2 , pp. 131-137
    • Petráš, I.1    Vinagre, B.2
  • 5
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • C.H. Lubich, "Discretized fractional calculus", SIAM J. on Mathematical Analysis 17 (3), 704-719 (1986
    • (1986) SIAM J. on Mathematical Analysis , vol.17 , Issue.3 , pp. 704-719
    • Lubich, C.H.1
  • 6
    • 0033899008 scopus 로고    scopus 로고
    • Introduction to fractional linear systems ii: Discrete-time case
    • M.D. Ortigueira, "Introduction to fractional linear systems ii: Discrete-time case", IEE Proc. on Vision, Image and Signal Processing 147 (1), 71-78 (2000
    • (2000) IEE Proc. on Vision, Image and Signal Processing , vol.147 , Issue.1 , pp. 71-78
    • Ortigueira, M.D.1
  • 7
    • 0034588716 scopus 로고    scopus 로고
    • The non-integer difference of the discrete-time function and its application to the control system synthesis
    • P. Ostalczyk, "The non-integer difference of the discrete-time function and its application to the control system synthesis", Int. J. Systems Science 31 (12), 1551-1561 (2000
    • (2000) Int. J. Systems Science , vol.31 , Issue.12 , pp. 1551-1561
    • Ostalczyk, P.1
  • 8
    • 84876695925 scopus 로고    scopus 로고
    • Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains
    • P. Ostalczyk, "Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains", Int. J. Applied Mathematics and Computer Science 22 (3), 533-538 (2012
    • (2012) Int. J. Applied Mathematics and Computer Science , vol.22 , Issue.3 , pp. 533-538
    • Ostalczyk, P.1
  • 9
    • 46149090068 scopus 로고    scopus 로고
    • The modelling and analysis of fractional-order control systems in discrete domain
    • I. Petráš, L. Dorčák, and I. Koštial, "The modelling and analysis of fractional-order control systems in discrete domain", Proc. Int. Carpatian Control Conf. 1, 257-260 (2000
    • (2000) Proc. Int. Carpatian Control Conf , vol.1 , pp. 257-260
    • Petráš, I.1    Dorčák, L.2    Koštial, I.3
  • 10
    • 52349085396 scopus 로고    scopus 로고
    • Stability of discrete fractional order state-space systems
    • A. Dzieliński and D. Sierociuk, "Stability of discrete fractional order state-space systems", J. Vibration and Control 14 (9-10), 1543-1556 (2008
    • (2008) J. Vibration and Control , vol.14 , Issue.9-10 , pp. 1543-1556
    • Dzieliński, A.1    Sierociuk, D.2
  • 11
    • 57749088785 scopus 로고    scopus 로고
    • Practical stability of positive fractional discretetime linear systems
    • T. Kaczorek, "Practical stability of positive fractional discretetime linear systems", Bull. Pol. Ac. Tech. 56 (4), 313-317 (2008
    • (2008) Bull. Pol. Ac. Tech , vol.56 , Issue.4 , pp. 313-317
    • Kaczorek, T.1
  • 12
    • 33646729035 scopus 로고    scopus 로고
    • Fractional Kalman filter algorithm for states, parameters and order of fractional system estimation
    • D. Sierociuk and A. Dzieliński, "Fractional Kalman filter algorithm for states, parameters and order of fractional system estimation", Int. J. Applied Mathematics and Computer Science 16 (1), 101-112 (2006
    • (2006) Int. J. Applied Mathematics and Computer Science , vol.16 , Issue.1 , pp. 101-112
    • Sierociuk, D.1    Dzieliński, A.2
  • 13
    • 84871018471 scopus 로고    scopus 로고
    • Normalized finite fractional differences: The computational and accuracy breakthroughs
    • R. Stanisławski and K.J. Latawiec, "Normalized finite fractional differences: The computational and accuracy breakthroughs", Int. J. Applied Mathematics and Computer Science 22 (4), 907-919 (2012
    • (2012) Int. J. Applied Mathematics and Computer Science , vol.22 , Issue.4 , pp. 907-919
    • Stanisławski, R.1    Latawiec, K.J.2
  • 14
    • 69149089847 scopus 로고    scopus 로고
    • Simple conditions for practical stability of positive fractional discrete-time linear systems
    • M. Busłowicz and T. Kaczorek, "Simple conditions for practical stability of positive fractional discrete-time linear systems", Int. J. Applied Mathematics and Computer Science 19 (2), 263-269 (2009
    • (2009) Int. J. Applied Mathematics and Computer Science , vol.19 , Issue.2 , pp. 263-269
    • Busłowicz, M.1    Kaczorek, T.2
  • 19
    • 78049484516 scopus 로고    scopus 로고
    • Modeling of open-loop stable linear systems using a combination of a finite fractional derivative and orthonormal basis functions
    • R. Stanisławski and K.J. Latawiec, "Modeling of open-loop stable linear systems using a combination of a finite fractional derivative and orthonormal basis functions", Proc. 15th Int. Conf. on Methods and Models in Automation and Robotics 1, 411-414 (2010
    • (2010) Proc. 15th Int. Conf. on Methods and Models in Automation and Robotics , vol.1 , pp. 411-414
    • Stanisławski, R.1    Latawiec, K.J.2
  • 20
    • 77954349733 scopus 로고    scopus 로고
    • Stability criteria for a class of fractional order systems
    • I. Kheirzad, M.S. Tavazoei, and A.A. Jalali, "Stability criteria for a class of fractional order systems", Nonlinear Dynamics 61 (1-2), 153-161 (2010
    • (2010) Nonlinear Dynamics , vol.61 , Issue.1-2 , pp. 153-161
    • Kheirzad, I.1    Tavazoei, M.S.2    Jalali, A.A.3
  • 21
    • 67650502609 scopus 로고    scopus 로고
    • Asymptotical stability analysis of linear fractional differential systems
    • C-p. Li and Z-g. Zhao, "Asymptotical stability analysis of linear fractional differential systems", J. Shanghai University (English Edition) 13 (3), 197-206 (2009
    • (2009) J. Shanghai University (English Edition , vol.13 , Issue.3 , pp. 197-206
    • Li, C.-P.1    Zhao, Z.-G.2
  • 22
    • 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", Computational Engineering in Systems Applications 2, 963-968 (1996
    • (1996) Computational Engineering in Systems Applications , vol.2 , pp. 963-968
    • Matignon, D.1
  • 23
    • 0000074512 scopus 로고    scopus 로고
    • Stability properties for generalized fractional differential systems
    • D. Matignon, "Stability properties for generalized fractional differential systems", ESAIM: Proc. 5, 145-158 (1998
    • (1998) ESAIM: Proc , vol.5 , pp. 145-158
    • Matignon, D.1
  • 24
    • 77954349836 scopus 로고    scopus 로고
    • Stability of fractional-order systems with rational orders: A survey
    • I. Petráš, "Stability of fractional-order systems with rational orders: A survey", Fractional Calculus and Applied Analysis 12 (3), 269-298 (2009
    • (2009) Fractional Calculus and Applied Analysis , vol.12 , Issue.3 , pp. 269-298
    • Petráš, I.1
  • 27
    • 84874771284 scopus 로고    scopus 로고
    • Simple stability conditions of linear discrete time systems with multiple delay
    • S.B. Stojanovic and D.L. Debeljkovic, "Simple stability conditions of linear discrete time systems with multiple delay", Serbian J. Electrical Engineering 7 (1), 69-79 (2010
    • (2010) Serbian J. Electrical Engineering , vol.7 , Issue.1 , pp. 69-79
    • Stojanovic, S.B.1    Debeljkovic, D.L.2
  • 28
    • 79951632060 scopus 로고    scopus 로고
    • Robust stability of positive discrete-time linear systems of fractional order
    • M. Busłowicz, "Robust stability of positive discrete-time linear systems of fractional order", Bull. Pol. Ac. Tech. 58 (4), 567-572 (2010
    • (2010) Bull. Pol. Ac. Tech , vol.58 , Issue.4 , pp. 567-572
    • Busłowicz, M.1
  • 29
    • 77952247093 scopus 로고    scopus 로고
    • Practical stability and asymptotic stability of positive fractional 2d linear systems
    • T. Kaczorek, "Practical stability and asymptotic stability of positive fractional 2d linear systems", Asian J. Control 12 (2), 200-207 (2010
    • (2010) Asian J. Control , vol.12 , Issue.2 , pp. 200-207
    • Kaczorek, T.1
  • 30
    • 84870659780 scopus 로고    scopus 로고
    • New stability tests of positive standard and fractional linear systems
    • T. Kaczorek, "New stability tests of positive standard and fractional linear systems", Circuits and Systems 2 (4), 261-268 (2011
    • (2011) Circuits and Systems , vol.2 , Issue.4 , pp. 261-268
    • Kaczorek, T.1
  • 36
    • 84872854593 scopus 로고    scopus 로고
    • New Laguerre filter approximators to the Grünwald-Letnikov fractional difference
    • R. Stanisławski, "New Laguerre filter approximators to the Grünwald-Letnikov fractional difference", Mathematical Problems in Engineering 2012, 732917 (2012
    • (2012) Mathematical Problems in Engineering , vol.2012 , pp. 732917
    • Stanisławski, R.1
  • 38
    • 84883473459 scopus 로고    scopus 로고
    • University of Nebraska at Kearney, Karney, [Online]. Available:
    • B.L. Willis, "Eigenvalues by row operations", University of Nebraska at Kearney, Karney, [Online]. Available: Http://www.unk.edu/ uploadedFiles/facstaff/profiles/willisb/eigens-by-row(1).pdf (2005
    • (2005) Eigenvalues by Row Operations
    • Willis, B.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.