Global input-to-state stability and stabilization of discrete-time piece-wise affine systems

M. Lazar; W.P.M.H. Heemels

doi:10.3182/20060607-3-IT-3902.00056

Global input-to-state stability and stabilization of discrete-time piece-wise affine systems

M. Lazar, W.P.M.H. Heemels

Research output: Contribution to journal › Conference article › Academic › peer-review

1 Citation (Scopus)

Abstract

This paper presents sufficient conditions for global Input-to-State (practical) Stability (ISpS) and stabilization of discrete-time, possibly discontinuous, Piece-Wise Affine (PWA) systems. Piece-wise quadratic candidate ISpS (ISS) Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrix inequalities, which can be solved efficiently. One of the advantages of using the ISpS framework is that the additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures, and the results apply to PWA systems in their full generality, i.e. non-zero affine terms are allowed in the regions in the partition whose closure contains the origin. Copyright © 2006 IFAC.

Original language	English
Pages (from-to)	296-301
Number of pages	6
Journal	IFAC Proceedings Volumes
Volume	39
Issue number	5
DOIs	https://doi.org/10.3182/20060607-3-IT-3902.00056 https://doi.org/10.1016/B978-008044613-4.50055-0
Publication status	Published - 1 Dec 2006
Event	2nd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2006 - Alghero, Italy Duration: 7 Jun 2006 → 9 Jun 2006 Conference number: 2

Keywords

Hybrid systems
Piece-wise affine systems
Robust stability
Stabilization methods

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title = "Global input-to-state stability and stabilization of discrete-time piece-wise affine systems",

abstract = "This paper presents sufficient conditions for global Input-to-State (practical) Stability (ISpS) and stabilization of discrete-time, possibly discontinuous, Piece-Wise Affine (PWA) systems. Piece-wise quadratic candidate ISpS (ISS) Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrix inequalities, which can be solved efficiently. One of the advantages of using the ISpS framework is that the additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures, and the results apply to PWA systems in their full generality, i.e. non-zero affine terms are allowed in the regions in the partition whose closure contains the origin. Copyright {\textcopyright} 2006 IFAC.",

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AU - Heemels, W.P.M.H.

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N2 - This paper presents sufficient conditions for global Input-to-State (practical) Stability (ISpS) and stabilization of discrete-time, possibly discontinuous, Piece-Wise Affine (PWA) systems. Piece-wise quadratic candidate ISpS (ISS) Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrix inequalities, which can be solved efficiently. One of the advantages of using the ISpS framework is that the additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures, and the results apply to PWA systems in their full generality, i.e. non-zero affine terms are allowed in the regions in the partition whose closure contains the origin. Copyright © 2006 IFAC.

AB - This paper presents sufficient conditions for global Input-to-State (practical) Stability (ISpS) and stabilization of discrete-time, possibly discontinuous, Piece-Wise Affine (PWA) systems. Piece-wise quadratic candidate ISpS (ISS) Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrix inequalities, which can be solved efficiently. One of the advantages of using the ISpS framework is that the additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures, and the results apply to PWA systems in their full generality, i.e. non-zero affine terms are allowed in the regions in the partition whose closure contains the origin. Copyright © 2006 IFAC.

KW - Hybrid systems

KW - Piece-wise affine systems

KW - Robust stability

KW - Stabilization methods

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EP - 301

JO - IFAC Proceedings Volumes

JF - IFAC Proceedings Volumes

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Y2 - 7 June 2006 through 9 June 2006

ER -

Global input-to-state stability and stabilization of discrete-time piece-wise affine systems

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Keywords

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