Conditions for stabilizability of linear switched systems
Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop sy...
Ausführliche Beschreibung
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| Autor*in: |
Minh, Vu Trieu [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
continuous time linear switched systems |
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| Anmerkung: |
© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011 |
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| Übergeordnetes Werk: |
Enthalten in: International Journal of Control, Automation and Systems - Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009, 9(2011), 1 vom: Feb., Seite 139-144 |
|---|---|
| Übergeordnetes Werk: |
volume:9 ; year:2011 ; number:1 ; month:02 ; pages:139-144 |
| Links: |
|---|
| DOI / URN: |
10.1007/s12555-011-0118-2 |
|---|
| Katalog-ID: |
SPR026336634 |
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| 520 | |a Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence. | ||
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| 700 | 1 | |a Parman, Setyamartana |4 aut | |
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10.1007/s12555-011-0118-2 doi (DE-627)SPR026336634 (SPR)s12555-011-0118-2-e DE-627 ger DE-627 rakwb eng Minh, Vu Trieu verfasserin aut Conditions for stabilizability of linear switched systems 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011 Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence. Common Lyapunov matrix (dpeaa)DE-He213 continuous time linear switched systems (dpeaa)DE-He213 discrete time switched linear systems (dpeaa)DE-He213 linear quadratic state feedback regulator (dpeaa)DE-He213 Awang, Mokhtar aut Parman, Setyamartana aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 9(2011), 1 vom: Feb., Seite 139-144 (DE-627)SPR026303256 nnns volume:9 year:2011 number:1 month:02 pages:139-144 https://dx.doi.org/10.1007/s12555-011-0118-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 9 2011 1 02 139-144 |
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10.1007/s12555-011-0118-2 doi (DE-627)SPR026336634 (SPR)s12555-011-0118-2-e DE-627 ger DE-627 rakwb eng Minh, Vu Trieu verfasserin aut Conditions for stabilizability of linear switched systems 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011 Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence. Common Lyapunov matrix (dpeaa)DE-He213 continuous time linear switched systems (dpeaa)DE-He213 discrete time switched linear systems (dpeaa)DE-He213 linear quadratic state feedback regulator (dpeaa)DE-He213 Awang, Mokhtar aut Parman, Setyamartana aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 9(2011), 1 vom: Feb., Seite 139-144 (DE-627)SPR026303256 nnns volume:9 year:2011 number:1 month:02 pages:139-144 https://dx.doi.org/10.1007/s12555-011-0118-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 9 2011 1 02 139-144 |
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10.1007/s12555-011-0118-2 doi (DE-627)SPR026336634 (SPR)s12555-011-0118-2-e DE-627 ger DE-627 rakwb eng Minh, Vu Trieu verfasserin aut Conditions for stabilizability of linear switched systems 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011 Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence. Common Lyapunov matrix (dpeaa)DE-He213 continuous time linear switched systems (dpeaa)DE-He213 discrete time switched linear systems (dpeaa)DE-He213 linear quadratic state feedback regulator (dpeaa)DE-He213 Awang, Mokhtar aut Parman, Setyamartana aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 9(2011), 1 vom: Feb., Seite 139-144 (DE-627)SPR026303256 nnns volume:9 year:2011 number:1 month:02 pages:139-144 https://dx.doi.org/10.1007/s12555-011-0118-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 9 2011 1 02 139-144 |
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10.1007/s12555-011-0118-2 doi (DE-627)SPR026336634 (SPR)s12555-011-0118-2-e DE-627 ger DE-627 rakwb eng Minh, Vu Trieu verfasserin aut Conditions for stabilizability of linear switched systems 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011 Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence. Common Lyapunov matrix (dpeaa)DE-He213 continuous time linear switched systems (dpeaa)DE-He213 discrete time switched linear systems (dpeaa)DE-He213 linear quadratic state feedback regulator (dpeaa)DE-He213 Awang, Mokhtar aut Parman, Setyamartana aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 9(2011), 1 vom: Feb., Seite 139-144 (DE-627)SPR026303256 nnns volume:9 year:2011 number:1 month:02 pages:139-144 https://dx.doi.org/10.1007/s12555-011-0118-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 9 2011 1 02 139-144 |
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10.1007/s12555-011-0118-2 doi (DE-627)SPR026336634 (SPR)s12555-011-0118-2-e DE-627 ger DE-627 rakwb eng Minh, Vu Trieu verfasserin aut Conditions for stabilizability of linear switched systems 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011 Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence. Common Lyapunov matrix (dpeaa)DE-He213 continuous time linear switched systems (dpeaa)DE-He213 discrete time switched linear systems (dpeaa)DE-He213 linear quadratic state feedback regulator (dpeaa)DE-He213 Awang, Mokhtar aut Parman, Setyamartana aut Enthalten in International Journal of Control, Automation and Systems Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers, 2009 9(2011), 1 vom: Feb., Seite 139-144 (DE-627)SPR026303256 nnns volume:9 year:2011 number:1 month:02 pages:139-144 https://dx.doi.org/10.1007/s12555-011-0118-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_21 GBV_ILN_24 GBV_ILN_72 GBV_ILN_181 GBV_ILN_496 GBV_ILN_2002 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2060 GBV_ILN_2470 AR 9 2011 1 02 139-144 |
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Conditions for stabilizability of linear switched systems |
| abstract |
Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence. © Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011 |
| abstractGer |
Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence. © Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011 |
| abstract_unstemmed |
Abstract This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence. © Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011 |
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| title_short |
Conditions for stabilizability of linear switched systems |
| url |
https://dx.doi.org/10.1007/s12555-011-0118-2 |
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| author2 |
Awang, Mokhtar Parman, Setyamartana |
| author2Str |
Awang, Mokhtar Parman, Setyamartana |
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| doi_str |
10.1007/s12555-011-0118-2 |
| up_date |
2024-07-03T20:19:42.620Z |
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