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Volumn 20, Issue 1, 2017, Pages 243-259

New results in stability analysis for LTI SISO systems modeled by GL-discretized fractional-order transfer functions

Author keywords

discrete time system; fractional order system; stability analysis

Indexed keywords


EID: 85014052715     PISSN: 13110454     EISSN: 13142224     Source Type: Journal    
DOI: 10.1515/fca-2017-0013     Document Type: Article
Times cited : (14)

References (31)
  • 1
    • 84879776323 scopus 로고    scopus 로고
    • On the asymptotic stability of linear system of fractional-order difference equations
    • R. Abu-Saris, Q. Al-Madallal, On the asymptotic stability of linear system of fractional-order difference equations. Fract. Calc. Appl. Anal. 16, No 1 (2013), 613-629; DOI: 10. 2478/s13540-013-0039-2; https://www. degruyter. com/view/j/fca. 2013. 16. issue-1/ issue-files/fca. 2013. 16. issue-1. xml.
    • (2013) Fract. Calc. Appl. Anal. , vol.16 , Issue.1 , pp. 613-629
    • Abu-Saris, R.1    Al-Madallal, Q.2
  • 2
    • 44649195602 scopus 로고    scopus 로고
    • Al-Alaoui operator and the new transformation polynomials for discretization of analogue systems
    • M. A. Al-Alaoui, Al-Alaoui operator and the new transformation polynomials for discretization of analogue systems. Electrical Engineering 90, No 6 (2008), 455-467; DOI: 10. 1007/s00202-007-0092-0.
    • (2008) Electrical Engineering , vol.90 , Issue.6 , pp. 455-467
    • Al-Alaoui, M.A.1
  • 3
    • 57749209882 scopus 로고    scopus 로고
    • Stability of linear continuous-time fractional order systems with delays of the retarded type
    • M. Buslowicz, Stability of linear continuous-time fractional order systems with delays of the retarded type. Bulletin of the Polish Academy of Sciences, Techn. Sciences 56, No 4 (2008), 319-324.
    • (2008) Bulletin of the Polish Academy of Sciences, Techn. Sciences , vol.56 , Issue.4 , pp. 319-324
    • Buslowicz, M.1
  • 4
    • 79951632060 scopus 로고    scopus 로고
    • Robust stability of positive discrete-time linear systems of fractional order
    • M. Buslowicz, Robust stability of positive discrete-time linear systems of fractional order. Bulletin of the Polish Academy of Sciences, Techn. Sciences 58, No 4 (2010), 567-572; DOI: 10. 2478/v10175-010-0057-8.
    • (2010) Bulletin of the Polish Academy of Sciences, Techn. Sciences , vol.58 , Issue.4 , pp. 567-572
    • Buslowicz, M.1
  • 5
    • 69149089847 scopus 로고    scopus 로고
    • Simple conditions for practical stability of positive fractional discrete-time linear systems
    • M. Buslowicz, T. Kaczorek, Simple conditions for practical stability of positive fractional discrete-time linear systems. Int. J. Appl. Math. Comput. Sci. 19, No 2 (2009), 263-269; DOI: 10. 2478/v10006-009-0022-6.
    • (2009) Int. J. Appl. Math. Comput. Sci. , vol.19 , Issue.2 , pp. 263-269
    • Buslowicz, M.1    Kaczorek, T.2
  • 6
    • 84934878757 scopus 로고    scopus 로고
    • On explicit stability conditions for a linear fractional difference system
    • J. Cernák, I. Györi, L. Nechvátal, On explicit stability conditions for a linear fractional difference system. Fract. Calc. Appl. Anal. 18, No 3 (2015), 651-672; DOI: 10. 1515/fca-2015-0040; https://www. degruyter. com/view/j/fca. 2015. 18. issue-3/ issue-files/fca. 2015. 18. issue-3. xml.
    • (2015) Fract. Calc. Appl. Anal. , vol.18 , Issue.3 , pp. 651-672
    • Cernák, J.1    Györi, I.2    Nechvátal, L.3
  • 7
    • 84990857128 scopus 로고    scopus 로고
    • Asymptotic stability of dynamic equations with two fractional terms: Continuous versus discrete case
    • J. Cernák, T. Kisela, Asymptotic stability of dynamic equations with two fractional terms: Continuous versus discrete case. Fract. Calc. Appl. Anal. 18, No 2 (2015), 437-458; DOI: 10. 1515/fca-2015-0028; https://www. degruyter. com/view/j/fca. 2015. 18. issue-2/ issue-files/fca. 2015. 18. issue-2. xml.
    • (2015) Fract. Calc. Appl. Anal. , vol.18 , Issue.2 , pp. 437-458
    • Cernák, J.1    Kisela, T.2
  • 8
    • 52349085396 scopus 로고    scopus 로고
    • Stability of discrete fractional order statespace systems
    • A. Dzielínski, D. Sierociuk, Stability of discrete fractional order statespace systems. J. Vib. Control 14, No 9-10 (2008), 1543-1556; DOI: 10. 1177/1077546307087431.
    • (2008) J. Vib. Control , vol.14 , Issue.9-10 , pp. 1543-1556
    • Dzielínski, A.1    Sierociuk, D.2
  • 9
    • 84910107177 scopus 로고    scopus 로고
    • A graphic stability criterion for non-commensurate fractionalorder time-delay systems
    • Z. Gao, A graphic stability criterion for non-commensurate fractionalorder time-delay systems. Nonlinear Dyn. 78, No 3 (2012), 2101-2111; DOI: 10. 1007/s11071-014-1580-1.
    • (2012) Nonlinear Dyn. , vol.78 , Issue.3 , pp. 2101-2111
    • Gao, Z.1
  • 11
    • 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, No 4 (2011), 261-268; DOI: 10. 4236/cs. 2011. 24036.
    • (2011) Circuits and Systems , vol.2 , Issue.4 , pp. 261-268
    • Kaczorek, T.1
  • 13
    • 84985006688 scopus 로고    scopus 로고
    • Responses comparison of the two discretetime linear fractional state-space models
    • T. Kaczorek, P. Ostalczyk, Responses comparison of the two discretetime linear fractional state-space models. Fract. Calc. Appl. Anal. 19, No 4 (2016), 789-805; DOI: 10. 1515/fca-2016-0043; https://www. degruyter. com/view/j/fca. 2016. 19. issue-4/ issue-files/fca. 2016. 19. issue-4. xml.
    • (2016) Fract. Calc. Appl. Anal. , vol.19 , Issue.4 , pp. 789-805
    • Kaczorek, T.1    Ostalczyk, P.2
  • 14
    • 1542496801 scopus 로고    scopus 로고
    • 2nd Ed. Addison Wesley Publishing Company, Boston, MA
    • R. Lopez, Advanced Engineering Mathematics, 2nd Ed. Addison Wesley Publishing Company, Boston, MA (2001).
    • (2001) Advanced Engineering Mathematics
    • Lopez, R.1
  • 15
    • 84871749893 scopus 로고    scopus 로고
    • Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties
    • J. G. Lu, Y. Q. Chen, Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties. Fract. Calc. Appl. Anal. 16, No 1 (2013), 142-157; DOI: 10. 2478/s13540-013-0010-2; https://www. degruyter. com/view/j/fca. 2013. 16. issue-1/ issue-files/fca. 2013. 16. issue-1. xml.
    • (2013) Fract. Calc. Appl. Anal. , vol.16 , Issue.1 , pp. 142-157
    • Lu, J.G.1    Chen, Y.Q.2
  • 16
    • 80053650360 scopus 로고    scopus 로고
    • Stability and resonance conditions of elementary fractional transfer functions
    • R. Malti, X. Moreau, F. Khemane, A. Oustaloup, Stability and resonance conditions of elementary fractional transfer functions. Automatica 47, No 11 (2011), 2462-2467; DOI: 10. 1016/j. Automatica. 2011. 08. 029.
    • (2011) Automatica , vol.47 , Issue.11 , pp. 2462-2467
    • Malti, R.1    Moreau, X.2    Khemane, F.3    Oustaloup, A.4
  • 17
    • 0002731965 scopus 로고    scopus 로고
    • Stability results for fractional differential equations with applications to control processing
    • Lille, France
    • D. Matignon, Stability results for fractional differential equations with applications to control processing. In: Computational Engineering in Systems and Applications Multiconference, Vol. 2, Lille, France (1996), 963-968.
    • (1996) Computational Engineering in Systems and Applications Multiconference , vol.2 , pp. 963-968
    • Matignon, D.1
  • 18
    • 0000074512 scopus 로고    scopus 로고
    • Stability properties for generalized fractional differential systems
    • D. Matignon, Stability properties for generalized fractional differential systems. ESAIM Proceedings 5 (1998), 145-158; DOI: 10. 1051/proc:1998004.
    • (1998) ESAIM Proceedings , vol.5 , pp. 145-158
    • Matignon, D.1
  • 20
    • 84925340769 scopus 로고    scopus 로고
    • The z-transform method and delta type fractional difference operators
    • D. Mozyrska, M. Wyrwas, The z-transform method and delta type fractional difference operators. Discrete Dyn. Nat. Soc. 2015 (2015), Article ID: 852734; DOI: 10. 1155/2015/852734.
    • (2015) Discrete Dyn. Nat. Soc. , vol.2015
    • Mozyrska, D.1    Wyrwas, M.2
  • 21
    • 84876695925 scopus 로고    scopus 로고
    • Equivalent descriptions of a discrete-time fractionalorder linear system and its stability domains
    • P. Ostalczyk, Equivalent descriptions of a discrete-time fractionalorder linear system and its stability domains. Int. J. Appl. Math. Comput. Sci. 22, No 3 (2012), 533-538; DOI: 10. 2478/v10006-012-0040-7.
    • (2012) Int. J. Appl. Math. Comput. Sci. , vol.22 , Issue.3 , pp. 533-538
    • Ostalczyk, P.1
  • 23
    • 77954349836 scopus 로고    scopus 로고
    • Stability of fractional-order systems with rational orders: A survey
    • I. Petrás, Stability of fractional-order systems with rational orders: A survey. Fract. Calc. Appl. Anal. 12, No 3 (2009), 269-298; at http://www. math. bas. bg/fcaa.
    • (2009) Fract. Calc. Appl. Anal. , vol.12 , Issue.3 , pp. 269-298
    • Petrás, I.1
  • 25
    • 78049331182 scopus 로고    scopus 로고
    • Stability preservation analysis in direct discretization of fractional order transfer functions
    • M. Siami, M. S. Tavazoei, M. Haeri, Stability preservation analysis in direct discretization of fractional order transfer functions. Signal Processing 91, No 3 (2011), 508-512; DOI: 10. 1016/j. sigpro. 2010. 06. 009.
    • (2011) Signal Processing , vol.91 , Issue.3 , pp. 508-512
    • Siami, M.1    Tavazoei, M.S.2    Haeri, M.3
  • 26
    • 84871018471 scopus 로고    scopus 로고
    • Normalized finite fractional differences-The computational and accuracy breakthroughs
    • R. Stanislawski, K. J. Latawiec, Normalized finite fractional differences-the computational and accuracy breakthroughs. Int. J. Appl. Math. Comput. Sci. 22, No 4 (2012), 907-919; DOI: 10. 2478/v10006-012-0067-9.
    • (2012) Int. J. Appl. Math. Comput. Sci. , vol.22 , Issue.4 , pp. 907-919
    • Stanislawski, R.1    Latawiec, K.J.2
  • 27
    • 84883470466 scopus 로고    scopus 로고
    • Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for asymptotic stability
    • R. Stanislawski, K. J. Latawiec, Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for asymptotic stability. Bull. of the Polish Academy of Sciences, Techn. Sciences 61, No 2 (2013), 353-361; DOI: 10. 2478/bpasts-2013-0034.
    • (2013) Bull. of the Polish Academy of Sciences, Techn. Sciences , vol.61 , Issue.2 , pp. 353-361
    • Stanislawski, R.1    Latawiec, K.J.2
  • 28
    • 84883475500 scopus 로고    scopus 로고
    • Stability analysis for discrete-time fractional-order LTI state-space systems. Part II: New stability criterion for FD-based systems
    • R. Stanislawski, K. J. Latawiec, Stability analysis for discrete-time fractional-order LTI state-space systems. Part II: New stability criterion for FD-based systems. Bull. of the Polish Academy of Sciences, Techn. Sciences 61, No 2 (2013), 362-370; DOI: 10. 2478/bpasts-2013-0035.
    • (2013) Bull. of the Polish Academy of Sciences, Techn. Sciences , vol.61 , Issue.2 , pp. 362-370
    • Stanislawski, R.1    Latawiec, K.J.2
  • 29
    • 84925337207 scopus 로고    scopus 로고
    • A comparative analysis of Laguerre-based approximators to the Grünwald-Letnikov fractionalorder difference
    • R. Stanislawski, K. J. Latawiec, M. lukaniszyn, A comparative analysis of Laguerre-based approximators to the Grünwald-Letnikov fractionalorder difference. Math. Probl. Eng. 2015 (2015), Article ID: 512104; DOI: 10. 1155/2015/512104.
    • (2015) Math. Probl. Eng. , vol.2015
    • Stanislawski, R.1    Latawiec, K.J.2    Lukaniszyn, M.3
  • 30
    • 84874771284 scopus 로고    scopus 로고
    • Simple stability conditions of linear discrete time systems with multiple delay
    • S. B. Stojanovic, D. L. Debeljkovic, Simple stability conditions of linear discrete time systems with multiple delay. Serbian J. of Electrical Engineering 7, No 1 (2010), 69-79; DOI: 10. 2298/SJEE1001069S.
    • (2010) Serbian J. of Electrical Engineering , vol.7 , Issue.1 , pp. 69-79
    • Stojanovic, S.B.1    Debeljkovic, D.L.2
  • 31
    • 84947017016 scopus 로고    scopus 로고
    • Stability analysis of impulsive fractional-order systems by vector comparison principle
    • R. Wu, M. Feckan, Stability analysis of impulsive fractional-order systems by vector comparison principle. Nonlinear Dyn. 82, No 4 (2015), 2007-2019; DOI: 10. 1007/s11071-015-2295-7.
    • (2015) Nonlinear Dyn. , vol.82 , Issue.4 , pp. 2007-2019
    • Wu, R.1    Feckan, M.2


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