Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

Magdi S. Mahmoud; Yan Shi; Fouad M. AL-Sunni

doi:10.1016/j.jfranklin.2009.02.010

Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

Magdi S. Mahmoud^*, Yan Shi, Fouad M. AL-Sunni

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H_∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.

Original language	English
Pages (from-to)	570-592
Number of pages	23
Journal	Journal of the Franklin Institute
Volume	346
Issue number	6
DOIs	https://doi.org/10.1016/j.jfranklin.2009.02.010
State	Published - Aug 2009

Bibliographical note

Funding Information:
The authors would like to thank anonymous reviewers for their constructive suggestions which helped in improving the readability of the paper. The support of KFUPM through research project IN080404 is acknowledged.

Keywords

Dissaptivity
Dissipative analysis
Dissipative synthesis
Nonlinear systems
State feedback
Time-delay systems

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications
Applied Mathematics

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10.1016/j.jfranklin.2009.02.010

Cite this

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title = "Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays",

abstract = "In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.",

keywords = "Dissaptivity, Dissipative analysis, Dissipative synthesis, Nonlinear systems, State feedback, Time-delay systems",

author = "Mahmoud, \{Magdi S.\} and Yan Shi and AL-Sunni, \{Fouad M.\}",

note = "Funding Information: The authors would like to thank anonymous reviewers for their constructive suggestions which helped in improving the readability of the paper. The support of KFUPM through research project IN080404 is acknowledged.",

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AU - Mahmoud, Magdi S.

AU - Shi, Yan

AU - AL-Sunni, Fouad M.

N1 - Funding Information: The authors would like to thank anonymous reviewers for their constructive suggestions which helped in improving the readability of the paper. The support of KFUPM through research project IN080404 is acknowledged.

PY - 2009/8

Y1 - 2009/8

N2 - In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.

AB - In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.

KW - Dissaptivity

KW - Dissipative analysis

KW - Dissipative synthesis

KW - Nonlinear systems

KW - State feedback

KW - Time-delay systems

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DO - 10.1016/j.jfranklin.2009.02.010

M3 - Article

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VL - 346

SP - 570

EP - 592

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 6

ER -

Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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