GLOBAL STABILIZATION OF LINEAR SYSTEMS WITH BOUNDED-CONTROLS USING STATE-DEPENDENT SATURATION FUNCTIONS
By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation func...
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| Published in | Journal of systems science and complexity Vol. 24; no. 3; pp. 477 - 490 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Beijing
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
01.06.2011
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1009-6124 1559-7067 |
| DOI | 10.1007/s11424-011-8325-8 |
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| Abstract | By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach. |
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| AbstractList | By using the so-called
SP
-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach. By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach. |
| Author | Bin ZHOU Guangren DUAN He KONG |
| AuthorAffiliation | Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China. |
| Author_xml | – sequence: 1 givenname: Bin surname: Zhou fullname: Zhou, Bin email: binzhou@hit.edu.cn, binzhouee@163.com organization: Center for Control Theory and Guidance Technology, Harbin Institute of Technology – sequence: 2 givenname: Guangren surname: Duan fullname: Duan, Guangren organization: Center for Control Theory and Guidance Technology, Harbin Institute of Technology – sequence: 3 givenname: He surname: Kong fullname: Kong, He organization: Center for Control Theory and Guidance Technology, Harbin Institute of Technology |
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| Cites_doi | 10.1002/(SICI)1099-1239(199709)7:9<835::AID-RNC216>3.0.CO;2-P 10.1109/9.981734 10.1201/9780203910818.ch4 10.1016/j.automatica.2004.07.001 10.1109/TAC.2007.910711 10.1109/9.533685 10.1109/TAC.2007.895956 10.1109/CDC.1991.261255 10.1109/TAC.2003.814276 10.1109/9.362853 10.1016/j.automatica.2005.07.004 10.1109/9.486638 10.1080/00207170701760144 10.1109/TAC.2004.837572 10.1016/0167-6911(92)90001-9 10.1016/0167-6911(93)90033-3 10.1007/978-1-4612-0205-9 10.1016/j.compstruc.2006.08.032 10.1109/TAC.2004.841128 |
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| Keywords | global stabilization stable polynomials Bounded feedback nonlinear control state-dependent saturation functions |
| Language | English |
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| Notes | By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach. Bounded feedback, global stabilization, nonlinear control, state-dependent saturation functions, SP-stable polynomials. 11-4543/O1 |
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| References_xml | – reference: CaoY.LinZ.WardD. G.An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturationIEEE Transactions on Automatic Control2002471140145187970210.1109/9.981734 – reference: MarchandN.HablyA.Global stabilization of multiple integrators with bounded controlAutomatica20054121472152217481110.1016/j.automatica.2005.07.0041100.93036 – reference: LinZ.SaberiA.Semi-global exponential stabilization of linear systems subject to ‘input saturation’ via linear feedbacksSystem & Control Letters1993213225239123533510.1016/0167-6911(93)90033-30788.93075 – reference: Z. Lin, Low Gain Feedback, Springer-Verlag, 1999. – reference: SaberiA.LinZ.TeelA. R.Control of linear systems with saturating actuatorsIEEE Transactions on Automatic Control1996413368378138298610.1109/9.4866380853.93046 – reference: H. J. Sussmann and Y. Yang, On the stabilizability of multiple integrators by means of bounded feedback controls, Proc. of the 30th Conference on Decision and Control, Brighton, England, December, 1991: 70–72. – reference: KalioraG.AstolfiA.Nonlinear control of feedforward systems with bounded signalsIEEE Transactions on Automatic Control2004491119751990210077510.1109/TAC.2004.837572 – reference: HuT.LinZ.Control Systems with Actuator Saturation: Analysis and Design2001BirkhauserBasel10.1007/978-1-4612-0205-91061.93003 – reference: TeelA. R.Global stabilization, and restricted tracking for multiple integrators with bounded controlsSystems & Control Letters1992183165171115322510.1016/0167-6911(92)90001-90752.93053 – reference: LanW.HuangJ.Semi-global stabilization and output regulation of singular linear systems with input saturationIEEE Trans. on Automatic Control200348712741280198810410.1109/TAC.2003.814276 – reference: DuH.LamJ.Energy-to-peak performance controller design for building via static output feedback under consideration of actuator saturationComputers and Structures Archive20068431–3222772290227335710.1016/j.compstruc.2006.08.032 – reference: ZhouB.DuanG. R.A novel nested non-linear feedback law for global stabilization of linear systems with bounded controlsInternational Journal of Control200881913521363242711410.1080/002071707017601441152.93487 – reference: MarchandN.HablyA.ChemoriA.Global stabilization with low computational cost of the discrete-time chain of integrators by means of bounded controlsIEEE Transactions on Automatic Control2007525948952232426110.1109/TAC.2007.895956 – reference: SuarezR.Alvarez-RamirezJ.Solis-DaunJ.Linear systems with bounded inputs: Global stabilization with eigenvalue placementInternational Journal of Robust and Nonlinear Control199779835846147037010.1002/(SICI)1099-1239(199709)7:9<835::AID-RNC216>3.0.CO;2-P0888.93050 – reference: LinZ.SaberiA.StoorvogelA. A.Semi-global stabilization of linear discrete-time systems subject to input saturation via linear feedback: An ARE-based approachIEEE Transactions on Automatic Control199641812031207140721010.1109/9.5336850873.93071 – reference: LinZ.LüL.Set invariance conditions for singular linear systems subject to actuator saturationIEEE Trans. on Automatic Control200752122351235510.1109/TAC.2007.910711 – reference: T. Iwasaki and M. Fu, Regional H2 performance synthesis, Actuator Saturation Control, Edited by V. Kapila and K. M. Grigoriadis, Marcel Dekker, 2001. – reference: GrimmG.TeelA. R.ZaccarianL.Linear LMI-based external anti-windup augmentation for stable linear systemsAutomatica20044019871996215600810.1016/j.automatica.2004.04.0141059.93048 – reference: SussmannH. J.SontagE. D.YangY.A general result on the stabilization of linear systems using bounded controlsIEEE Transactions on Automatic Control1994391224112425133756610.1109/9.3628530811.93046 – reference: Gomes da SilvaJ. M.JrTarbouriechS.Antiwindup design with guaranteed regions of stability: An LMI-based approachIEEE Transactions on Automatic Control2005501106111211081610.1109/TAC.2004.841128 – volume: 7 start-page: 835 issue: 9 year: 1997 ident: 8325_CR4 publication-title: International Journal of Robust and Nonlinear Control doi: 10.1002/(SICI)1099-1239(199709)7:9<835::AID-RNC216>3.0.CO;2-P – volume: 47 start-page: 140 issue: 1 year: 2002 ident: 8325_CR9 publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.981734 – ident: 8325_CR1 – ident: 8325_CR7 doi: 10.1201/9780203910818.ch4 – volume: 40 start-page: 1987 year: 2004 ident: 8325_CR8 publication-title: Automatica doi: 10.1016/j.automatica.2004.07.001 – volume: 52 start-page: 2351 issue: 12 year: 2007 ident: 8325_CR6 publication-title: IEEE Trans. on Automatic Control doi: 10.1109/TAC.2007.910711 – volume: 41 start-page: 1203 issue: 8 year: 1996 ident: 8325_CR11 publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.533685 – volume: 52 start-page: 948 issue: 5 year: 2007 ident: 8325_CR19 publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2007.895956 – ident: 8325_CR13 doi: 10.1109/CDC.1991.261255 – volume: 48 start-page: 1274 issue: 7 year: 2003 ident: 8325_CR5 publication-title: IEEE Trans. on Automatic Control doi: 10.1109/TAC.2003.814276 – volume: 39 start-page: 2411 issue: 12 year: 1994 ident: 8325_CR15 publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.362853 – volume: 41 start-page: 2147 year: 2005 ident: 8325_CR18 publication-title: Automatica doi: 10.1016/j.automatica.2005.07.004 – volume: 41 start-page: 368 issue: 3 year: 1996 ident: 8325_CR12 publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.486638 – volume: 81 start-page: 1352 issue: 9 year: 2008 ident: 8325_CR17 publication-title: International Journal of Control doi: 10.1080/00207170701760144 – volume: 49 start-page: 1975 issue: 11 year: 2004 ident: 8325_CR16 publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2004.837572 – volume: 18 start-page: 165 issue: 3 year: 1992 ident: 8325_CR14 publication-title: Systems & Control Letters doi: 10.1016/0167-6911(92)90001-9 – volume: 21 start-page: 225 issue: 3 year: 1993 ident: 8325_CR20 publication-title: System & Control Letters doi: 10.1016/0167-6911(93)90033-3 – volume-title: Control Systems with Actuator Saturation: Analysis and Design year: 2001 ident: 8325_CR2 doi: 10.1007/978-1-4612-0205-9 – volume: 84 start-page: 2277 issue: 31–32 year: 2006 ident: 8325_CR3 publication-title: Computers and Structures Archive doi: 10.1016/j.compstruc.2006.08.032 – volume: 50 start-page: 106 issue: 1 year: 2005 ident: 8325_CR10 publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2004.841128 |
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| Snippet | By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a... By using the so-called SP -stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a... |
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| Title | GLOBAL STABILIZATION OF LINEAR SYSTEMS WITH BOUNDED-CONTROLS USING STATE-DEPENDENT SATURATION FUNCTIONS |
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