Necessary and sufficient D-stability condition of fractional-order linear systems
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- 英文论文题名：Necessary and sufficient D-stability condition of fractional-order linear systems
- 论文作者：Keyong Shao ; Lipeng Zhou ; Kun Qian ; Yeqiang Yu ; Feng Chen ; Shuang Zheng
- 英文论文作者：Keyong Shao ; Lipeng Zhou ; Kun Qian ; Yeqiang Yu ; Feng Chen ; Shuang Zheng ; School of Electrical and Information Engineering ; Northeast Petroleum University ; School of Petroleum Engineering ; Northeast Petroleum University ; No.3 Oil Mine of The Third Oil Production Plant ; China National Petroleum Corporation
- 年：2017
- 作者机构：School of Electrical and Information Engineering, Northeast Petroleum University;School of Petroleum Engineering, Northeast Petroleum University;No.3 Oil Mine of The Third Oil Production Plant, China National Petroleum Corporation;
- 英文论文关键词：fractional-order linear system ; D-stability ; LMI region ; Linear matrix inequalities
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：259k
- 原文格式：D
- 会议级别：全国
摘要
This paper first discusses the D-pole placement problem of fractional-order linear systems. Some criteria are proposed to ensure that all the closed-loop eigenvalues of fractional-order linear systems are located inside a specific region S(a, r, θ).Then, necessary and sufficient D-stability condition of fractional-order linear systems guaranteeing the D-stability is presented.Conditions for feasibility are derived for a general class of convex regions of the complex plane. The result is obtained from the feasibility test of a set of linear matrix inequalities. Finally, illustrative example is given for demonstration.
This paper first discusses the D-pole placement problem of fractional-order linear systems. Some criteria are proposed to ensure that all the closed-loop eigenvalues of fractional-order linear systems are located inside a specific region S(a, r, θ).Then, necessary and sufficient D-stability condition of fractional-order linear systems guaranteeing the D-stability is presented.Conditions for feasibility are derived for a general class of convex regions of the complex plane. The result is obtained from the feasibility test of a set of linear matrix inequalities. Finally, illustrative example is given for demonstration.
This paper first discusses the D-pole placement problem of fractional-order linear systems. Some criteria are proposed to ensure that all the closed-loop eigenvalues of fractional-order linear systems are located inside a specific region S(a, r, θ).Then, necessary and sufficient D-stability condition of fractional-order linear systems guaranteeing the D-stability is presented.Conditions for feasibility are derived for a general class of convex regions of the complex plane. The result is obtained from the feasibility test of a set of linear matrix inequalities. Finally, illustrative example is given for demonstration.
引文
[1]Bagley,R.L.,&Calico,R.A.(1991).Calico,R.:fractional order state equations for the control of visco-elastically damped structures.Journal of Guidance Control&Dynamics,14(2),304-311.
[2]Rossikhin,Y.A.,&Shitikova,M.V.(1997).Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems.Acta Mechanica,120(1),109-125.
[3]Podlubny.I.(1999),Fractional Differential Equations.Academic Press,San Diego.
[4]Aoun,M.,Malti,R.,Levron,F.,&Oustaloup,A.(2007).Brief paper:synthesis of fractional laguerre basis for system approximation.Automatica,43(9),1640-1648.
[5]Monje,C.A.,Vinagre,B.M.,Feliu,V.,&Chen,Y.Q.(2008).Tuning and auto-tuning of fractional order controllers for industry applications.Control Engineering Practice,16(7),798-812.
[6]Tavazoei,M.S.,Haeri,M.,&Nazari,N.(2008).Analysis of undamped oscillations generated by marginally stable fractional order systems.Signal Processing,88(12),2971-2978.
[7]Vicino,A.(1989).Robustness of pole location in perturbed systems.Automatica,25(1),109-113.
[8]Kolla,S.R.,Yedavalli,R.K.,&Farison,J.B.(1989).Robust stability bounds on time-varying perturbations for statespace models of linear discrete-time systems.International Journal of Control,50(1),151-159.
[9]Chilali,M.,&Gahinet,P.(1996).H∞design with pole placement constraints:an lmi approach.IEEE Transactions on Automatic Control,41(3),358-367.
[10]Trigeassou,J.C.,Maamri,N.,Sabatier,J.,&Oustaloup,A.(2011).A lyapunov approach to the stability of fractional differential equations.Signal Processing,91(3),437-445..
[11]Hei,X.,&Wu,R.(2016).Finite-time stability of impulsive fractional-order systems with time-delay.Applied Mathematical Modelling,40(7C8),4285-4290.
[12]Li,Y.,Chen,Y.Q.,&Podlubny,I.(2009).Technical communique:mittag-leffler stability of fractional order nonlinear dynamic systems.Automatica,45(8),1965-1969.
[13]Tavakoli-Kakhki,M.,Haeri,M.,&Tavazoei,M.S.(2010).Over and under-convergent step responses in fractional-order transfer functions.Transactions of the Institute of Measurement&Control,32(4),376-394.
[14]Kuo,B.C.(1982).Automatic Control Systems.PrenticeHall.Englewood Cliffs,NJ.
[15]Ackermann,J.,Bartlett,A.,Kaesbauer,D.,Sienel,W.,&Steinhauser,R.(1993).Robust Control:Systems with Uncertain Physical Parameters.Springer-Verlag,New York,Inc.
[16]Anderson,B.,Bose,N.K.,&Jury,E.I.(1974).A simple test for zeros of a complex polynomial in a sector.IEEE Transactions on Automatic Control,19(4),437-438.
[17]Davison,E.,&Ramesh,N.(1970).A note on the eigenvalues of a real matrix.Automatic Control IEEE Transactions on,15(2),252-253.
[18]Matignon,D.(1997).Stability results for fractional differential equations with applications to control processing.Computational Engineering in Systems Applications,2,963–968.
[19]Tavazoei,M.S.,&Haeri,M.(2009).A note on the stability of fractional order systems.Mathematics&Computers in Simulation,79(5),1566-1576.
[20]Sabatier,J.,Moze,M.,&Farges,C.(2010).Lmi stability conditions for fractional order systems.Computers&Mathematics with Applications,59(5),1594-1609.
[2]Rossikhin,Y.A.,&Shitikova,M.V.(1997).Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems.Acta Mechanica,120(1),109-125.
[3]Podlubny.I.(1999),Fractional Differential Equations.Academic Press,San Diego.
[4]Aoun,M.,Malti,R.,Levron,F.,&Oustaloup,A.(2007).Brief paper:synthesis of fractional laguerre basis for system approximation.Automatica,43(9),1640-1648.
[5]Monje,C.A.,Vinagre,B.M.,Feliu,V.,&Chen,Y.Q.(2008).Tuning and auto-tuning of fractional order controllers for industry applications.Control Engineering Practice,16(7),798-812.
[6]Tavazoei,M.S.,Haeri,M.,&Nazari,N.(2008).Analysis of undamped oscillations generated by marginally stable fractional order systems.Signal Processing,88(12),2971-2978.
[7]Vicino,A.(1989).Robustness of pole location in perturbed systems.Automatica,25(1),109-113.
[8]Kolla,S.R.,Yedavalli,R.K.,&Farison,J.B.(1989).Robust stability bounds on time-varying perturbations for statespace models of linear discrete-time systems.International Journal of Control,50(1),151-159.
[9]Chilali,M.,&Gahinet,P.(1996).H∞design with pole placement constraints:an lmi approach.IEEE Transactions on Automatic Control,41(3),358-367.
[10]Trigeassou,J.C.,Maamri,N.,Sabatier,J.,&Oustaloup,A.(2011).A lyapunov approach to the stability of fractional differential equations.Signal Processing,91(3),437-445..
[11]Hei,X.,&Wu,R.(2016).Finite-time stability of impulsive fractional-order systems with time-delay.Applied Mathematical Modelling,40(7C8),4285-4290.
[12]Li,Y.,Chen,Y.Q.,&Podlubny,I.(2009).Technical communique:mittag-leffler stability of fractional order nonlinear dynamic systems.Automatica,45(8),1965-1969.
[13]Tavakoli-Kakhki,M.,Haeri,M.,&Tavazoei,M.S.(2010).Over and under-convergent step responses in fractional-order transfer functions.Transactions of the Institute of Measurement&Control,32(4),376-394.
[14]Kuo,B.C.(1982).Automatic Control Systems.PrenticeHall.Englewood Cliffs,NJ.
[15]Ackermann,J.,Bartlett,A.,Kaesbauer,D.,Sienel,W.,&Steinhauser,R.(1993).Robust Control:Systems with Uncertain Physical Parameters.Springer-Verlag,New York,Inc.
[16]Anderson,B.,Bose,N.K.,&Jury,E.I.(1974).A simple test for zeros of a complex polynomial in a sector.IEEE Transactions on Automatic Control,19(4),437-438.
[17]Davison,E.,&Ramesh,N.(1970).A note on the eigenvalues of a real matrix.Automatic Control IEEE Transactions on,15(2),252-253.
[18]Matignon,D.(1997).Stability results for fractional differential equations with applications to control processing.Computational Engineering in Systems Applications,2,963–968.
[19]Tavazoei,M.S.,&Haeri,M.(2009).A note on the stability of fractional order systems.Mathematics&Computers in Simulation,79(5),1566-1576.
[20]Sabatier,J.,Moze,M.,&Farges,C.(2010).Lmi stability conditions for fractional order systems.Computers&Mathematics with Applications,59(5),1594-1609.