A CAD-based algorithm for solving stable parameter region of fractional-order systems with structured perturbations

References

[1] S. Adelipour, A. Abooee, M. Haeri, LMI-based sufficient conditions for robust stability and stabilization of LTI-fractional-order systems subjected to interval and polytopic uncertainties. Trans. Inst. Meas. Control37, No 10 (2015), 1207–1216; 10.1177/0142331214559120.Suche in Google Scholar

[2] D.Q. Cao, Robust stability bounds for nonclassically damped systems with multi-directional perturbations. Int. J. Mech. Sci. 49, No 4 (2007), 405–413; 10.1016/j.ijmecsci.2006.09.018.Suche in Google Scholar

[3] L.P. Chen, R.C. Wu, Y.G. He, L.S. Yin, Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties. Appl. Math. Comput. 257, (2015), 274–284; 10.1016/j.amc.2014.12.103.Suche in Google Scholar

[4] S.K. Damarla, M. Kundu, Design of robust fractional PID controller using triangular strip operational matrices. Fract. Calc. Appl. Anal. 18, No 5 (2015), 1291–1326; 10.1515/fca-2015-0074; https://www.degruyter.com/view/j/fca.2015.18.issue-5/issue-files/fca.2015.18.issue-5.xml.Suche in Google Scholar

[5] S.S. Delshad, M.M. Asheghan, M.H. Beheshti, Robust stabilization of fractional-Order systems with interval uncertainties via fractional-order controllers. Adv. Differ. Equ. 2010, No 1 (2010), # 984601; 10.1155/2010/984601.Suche in Google Scholar

[6] D.S. Ding, D.L. Qi, Y. Meng, L. Xu, Adaptive Mittag-Leffler stabilization of commensurate fractional-order nonlinear systems. In: IEEE Conference on Decision and Control, Los Angeles, CA (2014), 6920–6926.10.1109/CDC.2014.7040476Suche in Google Scholar

[7] D.S. Ding, D.L. Qi, Q. Wang, Non-linear Mittag-Leffler stabilisation of commensurate fractional-order non-linear systems. IET Control Theory Appl. 9, No 5 (2015), 681–690; 10.1049/iet-cta.2014.0642.Suche in Google Scholar

[8] C. Farges, J. Sabatier, M. Moze, Fractional order polytopic systems: robust stability and stabilisation. Adv. Differ. Equ. 2011, No 1 (2011), 35; 10.1186/1687-1847-2011-35.Suche in Google Scholar

[9] Z. Gao, Robust stabilization criterion of fractional-order controllers for interval fractional-order plants. Automatica61 (2015), 9–17; 10.1016/j.automatica.2015.07.021.Suche in Google Scholar

[10] Z. Gao, X.Z. Liao, Robust stability criterion of fractional-order functions for interval fractional-order systems. IET Control Theory Appl. 7, No 1 (2013), 60–67; 10.1049/iet-cta.2011.0356.Suche in Google Scholar

[11] Z. Gao, L.R. Zhai, Y.D. Liu, Robust stabilizing regions of fractional-order PI^λ controllers for fractional-order systems with time-delays. Int. J. Autom. Comput. 14, No 3 (2017), 340–349; 10.1007/s11633-015-0941-7.Suche in Google Scholar

[12] E.N. Gryazina, B.T. Polyak, Stability regions in the parameter space: D-decomposition revisited. Automatica42, No 1 (2005), 13–26; 10.1016/j.automatica.2005.08.010.Suche in Google Scholar

[13] Z.Jiao, Y.S. Zhong, Robust stability for fractional-order systems with structured and unstructured uncertainties. Comput. Math. Appl. 64, No 10 (2012), 3258–3266; 10.1016/j.camwa.2012.03.011.Suche in Google Scholar

[14] Y.T. Juang, Z.C. Hong, Y.T. Wang, Pole-assignment for uncertain systems with structured perturbations. IEEE Trans. Circ. Syst. 37, No 1 (1990), 107–110; 10.1109/31.45697.Suche in Google Scholar

[15] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, North-Holland (2006).Suche in Google Scholar

[16] T.N. Liang, J.J. Chen, C. Lei, Algorithm of robust stability region for interval plant with time delay using fractional order PI^λD^μ controller. Commun. Nonlinear Sci. Numer. Simul. 17, No 2 (2012), 979–991; 10.1016/j.cnsns.2011.06.029.Suche in Google Scholar

[17] 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; 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.Suche in Google Scholar

[18] J.G. Lu, Y.Q. Chen, W.D Chen, Robust asymptotical stability of fractional-order linear systems with structured perturbations. Comput. Math. Appl. 66, No 5 (2013), 873–882; 10.1016/j.camwa.2013.03.001.Suche in Google Scholar

[19] Y.D. Ma, J.G. Lu, W.D. Chen, Robust stability and stabilization of fractional order linear systems with positive real uncertainty. ISA Trans. 53, No 2 (2014), 199–209; 10.1016/j.isatra.2013.11.013.Suche in Google Scholar PubMed

[20] K.A. Moornani, M. Haeri, Robust stability testing function and kharitonov-like theorem for fractional order interval systems. IET Control Theory Appl. 4, No 10 (2010), 2097–2108; 10.1049/iet-cta.2009.0485.Suche in Google Scholar

[21] T. Nusret, Ö.F. Özgüven, M.M. Özyetkin, Robust stability analysis of fractional order interval polynomials. ISA Trans. 48, No 2 (2009), 166–172; 10.1016/j.isatra.2009.01.002.Suche in Google Scholar PubMed

[22] I. Petráš, Tuning and implementation methods for fractional-order controllers. Fract. Calc. Appl. Anal. 15, No 2 (2012), 282–303; 10.2478/s13540-012-0021-4; https://www.degruyter.com/view/j/fca.2012.15.issue-2/issue-files/fca.2012.15.issue-2.xml.Suche in Google Scholar

[23] A.G. Radwan, A.M. Soliman, A.S. Elwakil, A. Sedeek, On the stability of linear systems with fractional-order elements. Chaos Soliton. Fract. 40, No 5 (2009), 2317–2328; 10.1016/j.chaos.2007.10.033.Suche in Google Scholar

[24] Y.H. Wei, Y.Q. Chen, S.S. Cheng, Y. Wang, Completeness on the stability criterion of fractional order LTI systems. Fract. Calc. Appl. Anal. 20, No 1 (2017), 159–172; 10.1515/fca-2017-0008; https://www.degruyter.com/view/j/fca.2017.20.issue-1/issue-files/fca.2017.20.issue-1.xml.Suche in Google Scholar