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

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Abstract

This article presents conditions for global input-to-state stability (ISS) and stabilization of discrete-time, possibly discontinuous, piecewise affine (PWA) systems. Piecewise quadratic, possibly discontinuous candidate ISS Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrixinequalities, which can be solved efficiently. One of the advantages of using the ISS framework is that additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures. Furthermore, 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.
Original languageEnglish
Pages (from-to)721-734
Number of pages14
JournalNonlinear Analysis: Hybrid Systems
Volume2
Issue number3
DOIs
Publication statusPublished - 2008

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Piecewise Affine Systems
Global Stability
Discrete-time
Stabilization
Synthesis
Lyapunov functions
Lyapunov Function
Closure
Disturbance
Partition
Sufficient Conditions
Term

Cite this

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title = "Global input-to-state stability and stabilization of discrete-time piecewise affine systems",
abstract = "This article presents conditions for global input-to-state stability (ISS) and stabilization of discrete-time, possibly discontinuous, piecewise affine (PWA) systems. Piecewise quadratic, possibly discontinuous candidate ISS Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrixinequalities, which can be solved efficiently. One of the advantages of using the ISS framework is that additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures. Furthermore, 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.",
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Global input-to-state stability and stabilization of discrete-time piecewise affine systems. / Lazar, M.; Heemels, W.P.M.H.

In: Nonlinear Analysis: Hybrid Systems, Vol. 2, No. 3, 2008, p. 721-734.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Global input-to-state stability and stabilization of discrete-time piecewise affine systems

AU - Lazar, M.

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

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N2 - This article presents conditions for global input-to-state stability (ISS) and stabilization of discrete-time, possibly discontinuous, piecewise affine (PWA) systems. Piecewise quadratic, possibly discontinuous candidate ISS Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrixinequalities, which can be solved efficiently. One of the advantages of using the ISS framework is that additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures. Furthermore, 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.

AB - This article presents conditions for global input-to-state stability (ISS) and stabilization of discrete-time, possibly discontinuous, piecewise affine (PWA) systems. Piecewise quadratic, possibly discontinuous candidate ISS Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrixinequalities, which can be solved efficiently. One of the advantages of using the ISS framework is that additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures. Furthermore, 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.

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DO - 10.1016/j.nahs.2007.11.005

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SP - 721

EP - 734

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JF - Nonlinear Analysis: Hybrid Systems

SN - 1751-570X

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