State feedback stabilization of discrete linear switching systems subject to nonsymmetrical state and control bounds
Stabilization problem of discrete-time linear switching systems with bounds on the state and control input is solved in this paper. First, the synthesis of state feedback controllers that ensure the stability of closed-loop switching systems is studied under a sufficient condition. By using the idea...
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| Published in | Journal of control theory and applications Vol. 10; no. 2; pp. 216 - 222 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
South China University of Technology and Academy of Mathematics and Systems Science, CAS
01.05.2012
Department of Control Science and Engineering, Harbin Institute of Technology, Harbin Heilongjiang 150001, China%Department of Control Science and Engineering, Jilin University, Changchun Jilin 130025, China |
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| Online Access | Get full text |
| ISSN | 1672-6340 1993-0623 |
| DOI | 10.1007/s11768-012-0104-0 |
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| Abstract | Stabilization problem of discrete-time linear switching systems with bounds on the state and control input is solved in this paper. First, the synthesis of state feedback controllers that ensure the stability of closed-loop switching systems is studied under a sufficient condition. By using the idea of positive invariance, a stabilizing controller design methodology is proposed. Based on these results, the convergence rate problem is also discussed. A state feedback controller that guarantees the optimal convergence rate of closed-loop switching systems is obtained via optimization. Finally, an example made up of two subsystems is studied to show the application of our method. |
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| AbstractList | Stabilization problem of discrete-time linear switching systems with bounds on the state and control input is solved in this paper. First, the synthesis of state feedback controllers that ensure the stability of closed-loop switching systems is studied under a sufficient condition. By using the idea of positive invariance, a stabilizing controller design methodology is proposed. Based on these results, the convergence rate problem is also discussed. A state feedback controller that guarantees the optimal convergence rate of closed-loop switching systems is obtained via optimization. Finally, an example made up of two subsystems is studied to show the application of our method. O231; Stabilization problem of discrete-time linear switching systems with bounds on the state and control input is solved in this paper.First,the synthesis of state feedback controllers that ensure the stability of closed-loop switching systems is studied under a sufficient condition.By using the idea of positive invariance,a stabilizing controller design methodology is proposed.Based on these results,the convergence rate problem is also discussed.A state feedback controller that guarantees the optimal convergence rate of closed-loop switching systems is obtained via optimization.Finally,an example made up of two subsystems is studied to show the application of our method. |
| Author | Liu, Zhiyuan Fan, Guowei Chen, Hong |
| AuthorAffiliation | Department of Control Science and Engineering, Harbin Institute of Technology, Harbin Heilongjiang 150001, China%Department of Control Science and Engineering, Jilin University, Changchun Jilin 130025, China |
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| Cites_doi | 10.1080/00207178808906339 10.1109/9.539424 10.1016/S0005-1098(99)00113-2 10.1080/00207178908953358 10.1109/CDC.1989.70671 10.1016/j.nahs.2007.11.007 10.1016/S0005-1098(98)00193-9 10.1080/00207178808906132 10.1109/9.664150 10.1080/00207170701280903 10.1109/TAC.2003.822860 10.1016/j.na.2005.12.040 |
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| Copyright | South China University of Technology, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2012 Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| DocumentTitleAlternate | State feedback stabilization of discrete linear switching systems subject to nonsymmetrical state and control bounds |
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| Keywords | Stabilization problem Convergence rate problem Switching systems Constraints |
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| Notes | 44-1600/TP Zhiyuan LIU 1, Guowei FAN 1, Hong CHEN 2 1.Department of Control Science and Engineering, Harbin Institute of Technology, Harbin Heilongjiang 150001, China; 2.Department of Control Science and Engineering, Jilin University, Changchun Jilin 130025, China Switching systems; Constraints; Stabilization problem; Convergence rate problem Stabilization problem of discrete-time linear switching systems with bounds on the state and control input is solved in this paper. First, the synthesis of state feedback controllers that ensure the stability of closed-loop switching systems is studied under a sufficient condition. By using the idea of positive invariance, a stabilizing controller design methodology is proposed. Based on these results, the convergence rate problem is also discussed. A state feedback controller that guarantees the optimal convergence rate of closed-loop switching systems is obtained via optimization. Finally, an example made up of two subsystems is studied to show the application of our method. ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
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| Publisher | South China University of Technology and Academy of Mathematics and Systems Science, CAS Department of Control Science and Engineering, Harbin Institute of Technology, Harbin Heilongjiang 150001, China%Department of Control Science and Engineering, Jilin University, Changchun Jilin 130025, China |
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| References_xml | – start-page: 1878 year: 2004 end-page: 1883 ident: CR4 article-title: Digital control of continuous-time switching systems with safety constraints publication-title: Proceedings of the 43rd IEEE Conference on Decision and Control – volume: 48 start-page: 2441 issue: 6 year: 1988 end-page: 2451 ident: CR9 article-title: Regulator problem for linear discretetime systems with non-symmetrical constrained control publication-title: International Journal of Control doi: 10.1080/00207178808906339 – volume: 41 start-page: 1413 issue: 10 year: 1996 end-page: 1431 ident: CR14 article-title: Supervisory control of families of linear set-point controllers — Part 1: exact matching publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.539424 – volume: 35 start-page: 1747 issue: 11 year: 1999 end-page: 1768 ident: CR11 article-title: Set invariance in control — a survey publication-title: Automatica doi: 10.1016/S0005-1098(99)00113-2 – volume: 50 start-page: 193 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104_CR7 publication-title: Nonlinear Analysis: Hybrid Systems doi: 10.1016/j.nahs.2007.11.007 – volume: 80 start-page: 1379 issue: 9 year: 2007 ident: 104_CR12 publication-title: International Journal of Control doi: 10.1080/00207170701280903 – volume: 49 start-page: 184 issue: 2 year: 2004 ident: 104_CR3 publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2003.822860 – start-page: 1 volume-title: Proceedings of the 15th Mediterranean Conference on Control and Automation year: 2007 ident: 104_CR16 – volume: 35 start-page: 1747 issue: 11 year: 1999 ident: 104_CR11 publication-title: Automatica doi: 10.1016/S0005-1098(99)00113-2 – volume: 41 start-page: 1413 issue: 10 year: 1996 ident: 104_CR14 publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.539424 – volume: 47 start-page: 1727 issue: 6 year: 1988 ident: 104_CR17 publication-title: International Journal of Control doi: 10.1080/00207178808906132 – volume: 50 start-page: 193 issue: 1 year: 1989 ident: 104_CR15 publication-title: International Journal of Control doi: 10.1080/00207178908953358 – ident: 104_CR8 |
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| SubjectTerms | Complexity Computational Intelligence Control Control and Systems Theory Control systems Controllers Convergence Design engineering Engineering Mechatronics Optimization Robotics Stabilization State feedback Switching Systems Theory 控制输入 最优收敛速度 状态反馈控制器 状态反馈镇定 离散时间 稳定性 线性切换系统 非对称 |
| Title | State feedback stabilization of discrete linear switching systems subject to nonsymmetrical state and control bounds |
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