IEEE/CAA Journal of Automatica Sinica
Citation:  Reza Mohsenipour and Xinzhi Liu, "Robust DStability Test of LTI General Fractional Order Control Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 853864, May 2020. doi: 10.1109/JAS.2020.1003159 
[1] 
K. Diethelm, The Analysis of Fractional Differential Equations: An ApplicationOriented Exposition Using Differential Operators of Caputo Type. SpringerVerlag, 2010.

[2] 
J. Xu and J. Li, “Stochastic dynamic response and reliability assessment of controlled structures with fractional derivative model of viscoelastic dampers,” Mech. Syst. Sig. Process., vol. 72, pp. 865–896, 2016.

[3] 
I. N. Doye, K. N. Salama, and T. M. LalegKirati, “Robust fractionalorder proportionalintegral observer for synchronization of chaotic fractionalorder systems,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 268–277, 2019. doi: 10.1109/JAS.2017.7510874

[4] 
J. Liang and Y. Q. Chen, “Hybrid symbolic and numerical simulation studies of timefractional order wavediffusion systems,” Int. J. Control, vol. 79, no. 11, pp. 1462–1470, 2006. doi: 10.1080/00207170600726493

[5] 
C. Ionescu, A. Lopes, D. Copot, J. A. T. Machado, and J. H. T. Bates, “The role of fractional calculus in modeling biological phenomena: A review,” Commun. Nonlinear Sci. Numer. Simul., vol. 51, pp. 141–159, 2017. doi: 10.1016/j.cnsns.2017.04.001

[6] 
H. Yang, F. Wang, and F. Han, “Containment control of fractional order multiagent systems with time delays,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 3, pp. 727–732, 2018. doi: 10.1109/JAS.2016.7510211

[7] 
J. Huang, Y. Chen, H. Li, and X. Shi, “Fractional order modeling of human operator behavior with second order controlled plant and experiment research,” IEEE/CAA J. Autom. Sinica, vol. 3, no. 3, pp. 271–280, 2016. doi: 10.1109/JAS.2016.7508802

[8] 
Y. Zhao, Y. Li, F. Zhou, Z. Zhou, and Y. Q. Chen, “An iterative learning approach to identify fractional order KiBaM model,” IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 322–331, 2017. doi: 10.1109/JAS.2017.7510358

[9] 
R. Mohsenipour, “Robust performance control of space tether deployment using fractional order tension law,” J. Guid. Control Dyn., vol. 43, no. 2, pp. 347–353, 2020. doi: 10.2514/1.G004304

[10] 
C. A. Monje, B. M. Vinagre, V. Feliu, and Y. Q. Chen, “Tuning and autotuning of fractional order controllers for industry applications,” Control Eng. Pract., vol. 16, no. 7, pp. 798–812, 2008. doi: 10.1016/j.conengprac.2007.08.006

[11] 
C. Hua, T. Zhang, Y. Li, and X. Guan, “Robust output feedback control for fractional order nonlinear systems with timevarying delays,” IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 477–482, 2016. doi: 10.1109/JAS.2016.7510106

[12] 
R. Mohsenipour and M. FathiJegarkandi, “Fractional order MIMO controllers for robust performance of airplane longitudinal motion,” Aerosp. Sci. Technol., vol. 91, pp. 617–626, 2019. doi: 10.1016/j.ast.2019.06.036

[13] 
Z. Liao, C. Peng, W. Li, and Y. Wang, “Robust stability analysis for a class of fractional order systems with uncertain parameters,” J. Franklin Inst., vol. 348, no. 6, pp. 1101–1113, 2011. doi: 10.1016/j.jfranklin.2011.04.012

[14] 
I. NDoye, M. Darouach, M. Zasadzinski, and N. E. Radhy, “Robust stabilization of uncertain descriptor fractionalorder systems,” Automatica, vol. 49, no. 6, pp. 1907–1913, 2013. doi: 10.1016/j.automatica.2013.02.066

[15] 
J. G. Lu and Y. A. Zhao, “Decentralised robust H _{∞} control of fractionalorder interconnected systems with uncertainties,” Int. J. Control, vol. 90, no. 6, pp. 1221–1229, 2017. doi: 10.1080/00207179.2016.1201595

[16] 
J. G. Lu and G. Chen, “Robust stability and stabilization of fractionalorder interval systems: An LMI approach,” IEEE Trans. Autom. Control, vol. 54, no. 6, pp. 1294–1299, 2009. doi: 10.1109/TAC.2009.2013056

[17] 
S. Marir and M. Chadli, “Robust admissibility and stabilization of uncertain singular fractionalorder linear timeinvariant systems,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 685–692, 2019. doi: 10.1109/JAS.2019.1911480

[18] 
B. Aguiar, T. Gonzalez, and M. Bernal, “Comments on “robust stability and stabilization of fractionalorder interval systems with the fractional order α: The 0 < α < 1 case”,” IEEE Trans. Autom. Control, vol. 60, no. 2, pp. 582–583, 2015. doi: 10.1109/TAC.2014.2332711

[19] 
M. Góra and D. Mielczarek, “Comments on “necessary and sufficient stability condition of fractionalorder interval linear systems”[Automatica 44(2008), 2985–2988],” Automatica, vol. 50, no. 10, pp. 2734–2735, 2014. doi: 10.1016/j.automatica.2014.08.013

[20] 
B. B. Alagoz, “A note on robust stability analysis of fractional order interval systems by minimum argument vertex and edge polynomials,” IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 411–421, 2016. doi: 10.1109/JAS.2016.7510088

[21] 
H. Taghavian and M. S. Tavazoei, “Robust stability analysis of uncertain multiorder fractional systems: Young and Jensen inequalities approach,” Int. J. Robust Nonlinear Control, vol. 28, no. 4, pp. 1127–1144, 2018. doi: 10.1002/rnc.3919

[22] 
N. Tan, Ö. Faruk Özgüven, and M. Mine Özyetkin, “Robust stability analysis of fractional order interval polynomials,” ISA Trans., vol. 48, no. 2, pp. 166–172, 2009. doi: 10.1016/j.isatra.2009.01.002

[23] 
K. AkbariMoornani and M. Haeri, “Robust stability testing function and Kharitonovlike theorem for fractional order interval systems,” IET Control Theory Appl., vol. 4, no. 10, pp. 2097–2108, 2010. doi: 10.1049/ietcta.2009.0485

[24] 
Z. Gao and X. Liao, “Robust stability criterion of fractionalorder functions for interval fractionalorder systems,” IET Control Theory Appl., vol. 7, no. 1, pp. 60–67, 2013. doi: 10.1049/ietcta.2011.0356

[25] 
Z. Gao, “Robust stabilization criterion of fractionalorder controllers for interval fractionalorder plants,” Automatica, vol. 61, pp. 9–17, 2015. doi: 10.1016/j.automatica.2015.07.021

[26] 
C. Yeroglu and B. Senol, “Investigation of robust stability of fractional order multilinear affine systems: 2qconvex parpolygon approach,” Syst. Control Lett., vol. 62, no. 10, pp. 845–855, 2013. doi: 10.1016/j.sysconle.2013.06.005

[27] 
K. AkbariMoornani and M. Haeri, “On robust stability of linear time invariant fractionalorder systems with real parametric uncertainties,” ISA Trans., vol. 48, no. 4, pp. 484–490, 2009. doi: 10.1016/j.isatra.2009.04.006

[28] 
S. Zheng, “Robust stability of fractional order system with general interval uncertainties,” Syst. Control Lett., vol. 99, pp. 1–8, 2017. doi: 10.1016/j.sysconle.2016.11.001

[29] 
S. Zheng and W. Li, “Stabilizing region of PD^{μ} controller for fractional order system with general interval uncertainties and an interval delay,” J. Franklin Inst., vol. 355, no. 3, pp. 1107–1138, 2018. doi: 10.1016/j.jfranklin.2017.12.020

[30] 
G. Chesi, “Parameter and controller dependent Lyapunov functions for robust Dstability and robust performance controller design,” IEEE Trans. Autom. Control, vol. 62, no. 9, pp. 4798–4803, 2017. doi: 10.1109/TAC.2017.2692559

[31] 
C. Bonnet and J. R. Partington, “Analysis of fractional delay systems of retarded and neutral type,” Automatica, vol. 38, no. 7, pp. 1133–1138, 2002. doi: 10.1016/S00051098(01)003065

[32] 
S. Zheng, X. Tang, and B. Song, “Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust Dstability,” Int. J. Robust Nonlinear Control, vol. 26, no. 5, pp. 1112–1142, 2016. doi: 10.1002/rnc.3363

[33] 
R. Mohsenipour and M. FathiJegarkandi, “Robust Dstability testing function for LTI fractional order interval systems, ” in Proc. IEEE Conf. Control Technol. Appl., pp. 1277–1282, 2018.

[34] 
R. Mohsenipour and M. FathiJegarkandi, “Robust Dstability analysis of fractional order interval systems of commensurate and incommensurate orders,” IET Control Theory Appl., vol. 13, no. 8, pp. 1039–1050, 2019. doi: 10.1049/ietcta.2018.5111

[35] 
R. Mohsenipour and M. FathiJegarkandi, “A comment on “algorithm of robust stability region for interval plant with time delay using fractional order PI^{λ}D^{μ} controller” [Commun. Nonlinear Sci. Numer. Simul. 17(2012) 979–991],” Commun. Nonlinear Sci. Numer. Simul., vol. 63, pp. 202–204, 2018. doi: 10.1016/j.cnsns.2018.03.008

[36] 
K. AkbariMoornani and M. Haeri, “On robust stability of LTI fractionalorder delay systems of retarded and neutral type,” Automatica, vol. 46, no. 2, pp. 362–368, 2010. doi: 10.1016/j.automatica.2009.11.006

[37] 
R. J. Minnichelli, J. J. Anagnost, and C. A. Desoer, “An elementary proof of Kharitonov’s stability theorem with extensions,” IEEE Trans. Autom. Control, vol. 34, no. 9, pp. 995–998, 1989. doi: 10.1109/9.35816

[38] 
F. L. Janssens and J. C. van der Ha, “Stability of spinning satellite under axial thrust, internal mass motion, and damping,” J. Guid. Control Dyn., vol. 38, no. 4, pp. 761–771, 2015. doi: 10.2514/1.G000123

[39] 
Z. Alam, L. Yuan, and Q. Yang, “Chaos and combination synchronization of a new fractionalorder system with two stable nodefoci,” IEEE/CAA J. Autom. Sinica, vol. 3, no. 2, pp. 157–164, 2016. doi: 10.1109/JAS.2016.7451103

[40] 
B. Senol, A. Ates, B. Baykant Alagoz, and C. Yeroglu, “A numerical investigation for robust stability of fractionalorder uncertain systems,” ISA Trans., vol. 53, no. 2, pp. 189–198, 2014. doi: 10.1016/j.isatra.2013.09.004

[41] 
S. J. Chen and J. L. Lin, “Robust Dstability of discrete and continuous time interval systems,” J. Franklin Inst., vol. 341, no. 6, pp. 505–517, 2004. doi: 10.1016/j.jfranklin.2004.05.002

[42] 
M. Marden, Geometry of Polynomials. No. 3, American Mathematical Society, 2 ed., 1966.

[43] 
G. Sun and Z. H. Zhu, “Fractionalorder tension control law for deployment of space tether system,” J. Guid. Control Dyn., vol. 37, no. 6, pp. 2057–2061, 2014. doi: 10.2514/1.G000496

[44] 
S. Pradeep, “A new tension control law for deployment of tethered satellites,” Mech. Res. Commun., vol. 24, no. 3, pp. 247–254, 1997. doi: 10.1016/S00936413(97)000219

[45] 
O. Y. Viro, O. A. Ivanov, N. Y. Netsvetaev, and V. M. Kharlamov, Elementary Topology: Problem Textbook. American Mathematical Society, 2008.

[46] 
N. G. Lloyd, “Remarks on generalising Rouché’s theorem,” J. London Math. Soc., vol. s2–20, no. 2, pp. 259–272, 1979. doi: 10.1112/jlms/s220.2.259
