메뉴 건너뛰기




Volumn 45, Issue 8, 2009, Pages 1886-1890

A proof for non existence of periodic solutions in time invariant fractional order systems

Author keywords

Fractional calculus; Fractional order system; Periodic solution

Indexed keywords

FRACTIONAL CALCULUS; FRACTIONAL ORDER; FRACTIONAL ORDER DERIVATIVES; FRACTIONAL ORDER SYSTEM; FRACTIONAL-ORDER SYSTEMS; INTEGER ORDER; INTEGER-ORDER COUNTERPARTS; LIMIT CYCLE; NON-EXISTENCE; PERIODIC SIGNAL; PERIODIC SOLUTION; TIME INVARIANTS;

EID: 67649623211     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2009.04.001     Document Type: Article
Times cited : (191)

References (31)
  • 2
    • 0038818452 scopus 로고    scopus 로고
    • Control of chaos: methods and applications. Part I: methods
    • Andrievsky B.R., and Fradkov A.L. Control of chaos: methods and applications. Part I: methods. Automation and Remote Control 64 5 (2003) 673-713
    • (2003) Automation and Remote Control , vol.64 , Issue.5 , pp. 673-713
    • Andrievsky, B.R.1    Fradkov, A.L.2
  • 3
    • 34547597044 scopus 로고    scopus 로고
    • Synthesis of fractional Laguerre basis for system approximation
    • Aoun M., Malti R., Levron F., and Oustaloup A. Synthesis of fractional Laguerre basis for system approximation. Automatica 43 (2007) 1640-1648
    • (2007) Automatica , vol.43 , pp. 1640-1648
    • Aoun, M.1    Malti, R.2    Levron, F.3    Oustaloup, A.4
  • 4
    • 15544379984 scopus 로고    scopus 로고
    • Numerical simulations of fractional systems: An overview of existing methods and improvements
    • Aoun M., Malti R., Levron F., and Oustaloup A. Numerical simulations of fractional systems: An overview of existing methods and improvements. Nonlinear Dynamics 38 (2004) 117-131
    • (2004) Nonlinear Dynamics , vol.38 , pp. 117-131
    • Aoun, M.1    Malti, R.2    Levron, F.3    Oustaloup, A.4
  • 8
    • 33845961350 scopus 로고    scopus 로고
    • Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives
    • Daftardar-Gejji V., and Jafari H. Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives. Journal of Mathematical Analysis and Applications 328 (2007) 1026-1033
    • (2007) Journal of Mathematical Analysis and Applications , vol.328 , pp. 1026-1033
    • Daftardar-Gejji, V.1    Jafari, H.2
  • 10
    • 60749097464 scopus 로고    scopus 로고
    • Smith predictor based robust fractional order control: Application to water distribution in a main irrigation canal pool
    • Feliu-Batlle V., Rivas Pérez R., Castillo García F.G., and Sanchez Rodríguez L. Smith predictor based robust fractional order control: Application to water distribution in a main irrigation canal pool. Journal of Process Control 19 3 (2009) 506-519
    • (2009) Journal of Process Control , vol.19 , Issue.3 , pp. 506-519
    • Feliu-Batlle, V.1    Rivas Pérez, R.2    Castillo García, F.G.3    Sanchez Rodríguez, L.4
  • 11
    • 45449085216 scopus 로고    scopus 로고
    • Stability analysis and limit cycle in fractional system with Brusselator nonlinearities
    • Gafiychuk V., and Datsko B. Stability analysis and limit cycle in fractional system with Brusselator nonlinearities. Physics Letters A 372 (2008) 4902-4904
    • (2008) Physics Letters A , vol.372 , pp. 4902-4904
    • Gafiychuk, V.1    Datsko, B.2
  • 13
    • 44349159997 scopus 로고    scopus 로고
    • A limit cycle approach for the parametric identification of hysteretic systems
    • Ikhouane F., and Gomis-Bellmunt O. A limit cycle approach for the parametric identification of hysteretic systems. Systems & Control Letters 57 (2008) 663-669
    • (2008) Systems & Control Letters , vol.57 , pp. 663-669
    • Ikhouane, F.1    Gomis-Bellmunt, O.2
  • 14
    • 0034517069 scopus 로고    scopus 로고
    • Fractional market dynamics
    • Laskin N. Fractional market dynamics. Physica A 287 (2000) 482-492
    • (2000) Physica A , vol.287 , pp. 482-492
    • Laskin, N.1
  • 15
  • 16
    • 41549148741 scopus 로고    scopus 로고
    • Tuning and auto-tuning of fractional order controllers for industry applications
    • Monje C.A., Vinagre B.M., Feliu V., and Chen Y.Q. Tuning and auto-tuning of fractional order controllers for industry applications. Control Engineering Practice 16 (2008) 798-812
    • (2008) Control Engineering Practice , vol.16 , pp. 798-812
    • Monje, C.A.1    Vinagre, B.M.2    Feliu, V.3    Chen, Y.Q.4
  • 19
    • 0035848144 scopus 로고    scopus 로고
    • Control of chaos via an unstable delayed feedback controller
    • Pyragas K. Control of chaos via an unstable delayed feedback controller. Physics Review Letters 86 (2001) 2265-2268
    • (2001) Physics Review Letters , vol.86 , pp. 2265-2268
    • Pyragas, K.1
  • 20
    • 0030736195 scopus 로고    scopus 로고
    • Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass system
    • Rossikhin Y.A., and Shitikova M.V. Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass system. Acta Mechanica 120 (1997) 109-125
    • (1997) Acta Mechanica , vol.120 , pp. 109-125
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 21
    • 37549042003 scopus 로고    scopus 로고
    • Unreliability of Frequency Domain Approximation in Recognising Chaos in Fractional Order Systems
    • Tavazoei M.S., and Haeri M. Unreliability of Frequency Domain Approximation in Recognising Chaos in Fractional Order Systems. IET Signal Processing 1 4 (2007) 171-181
    • (2007) IET Signal Processing , vol.1 , Issue.4 , pp. 171-181
    • Tavazoei, M.S.1    Haeri, M.2
  • 23
    • 50049123574 scopus 로고    scopus 로고
    • Analysis of undamped oscillations generated by marginally stable fractional order systems
    • Tavazoei M.S., Haeri M., and Nazari N. Analysis of undamped oscillations generated by marginally stable fractional order systems. Signal Processing 88 (2008) 2971-2978
    • (2008) Signal Processing , vol.88 , pp. 2971-2978
    • Tavazoei, M.S.1    Haeri, M.2    Nazari, N.3
  • 24
    • 67649624652 scopus 로고    scopus 로고
    • Stability preservation analysis for frequency-based methods in numerical simulation of fractional order systems
    • Tavazoei M.S., Haeri M., Bolouki S., and Siami M. Stability preservation analysis for frequency-based methods in numerical simulation of fractional order systems. SIAM Journal on Numerical Analysis 47 1 (2008) 321-338
    • (2008) SIAM Journal on Numerical Analysis , vol.47 , Issue.1 , pp. 321-338
    • Tavazoei, M.S.1    Haeri, M.2    Bolouki, S.3    Siami, M.4
  • 25
    • 51249088596 scopus 로고    scopus 로고
    • Chaotic attractors in incommensurate fractional order systems
    • Tavazoei M.S., and Haeri M. Chaotic attractors in incommensurate fractional order systems. Physica D 237 (2008) 2628-2637
    • (2008) Physica D , vol.237 , pp. 2628-2637
    • Tavazoei, M.S.1    Haeri, M.2
  • 26
    • 66249115324 scopus 로고    scopus 로고
    • More details on analysis of fractional-order van der Pol oscillator
    • in press, doi:10.1177/1077546308096101
    • Tavazoei, M. S., Haeri, M., Attari, M., Bolouki, S., & Siami, M. (2009). More details on analysis of fractional-order van der Pol oscillator. Journal of Vibration and Control (in press). doi:10.1177/1077546308096101
    • (2009) Journal of Vibration and Control
    • Tavazoei, M.S.1    Haeri, M.2    Attari, M.3    Bolouki, S.4    Siami, M.5
  • 28
    • 33847067879 scopus 로고    scopus 로고
    • Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle?
    • Wang Y., and Li C. Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle?. Physics Letters A 363 (2007) 414-419
    • (2007) Physics Letters A , vol.363 , pp. 414-419
    • Wang, Y.1    Li, C.2
  • 31
    • 33845868440 scopus 로고    scopus 로고
    • Computation of limit cycles - the second part of Hilbert's 16th problem
    • Yu P. Computation of limit cycles - the second part of Hilbert's 16th problem. The Fields Institute Communications 49 (2006) 151-177
    • (2006) The Fields Institute Communications , vol.49 , pp. 151-177
    • Yu, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.