Asymptotically non-expansive self-maps and global stability with ultimate boundedness of dynamic systems

M. De La Sen; A. Ibeas

doi:https://doi.org/10.1016/j.amc.2013.04.009

Asymptotically non-expansive self-maps and global stability with ultimate boundedness of dynamic systems

M. De La Sen, A. Ibeas

Department of Telecommunications and Systems Engineering

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

5 Citations (Scopus)

Abstract

This paper investigates self-maps T: X → X which satisfy a distance constraint in a metric space with mixed point-dependent non-expansive properties or, in particular, contractive ones, and potentially expansive properties related to some distance threshold. The above mentioned constraint is feasible in certain real-world problems of usefulness, for instance, when discussing ultimate boundedness in dynamic systems which guarantees Lyapunov stability. This fact makes the proposed analysis to be potentially useful to investigate global stability properties in dynamic systems in the potential presence of some locally unstable equilibrium points. The results can be applied to stability problems of dynamics systems and circuit theory as the given examples suggest. © 2013 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	10655-10667
Journal	Applied Mathematics and Computation
Volume	219
DOIs	https://doi.org/10.1016/j.amc.2013.04.009
Publication status	Published - 6 May 2013

Keywords

Contractive maps
Fixed points
Metric space
Non-expansive maps

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title = "Asymptotically non-expansive self-maps and global stability with ultimate boundedness of dynamic systems",

abstract = "This paper investigates self-maps T: X → X which satisfy a distance constraint in a metric space with mixed point-dependent non-expansive properties or, in particular, contractive ones, and potentially expansive properties related to some distance threshold. The above mentioned constraint is feasible in certain real-world problems of usefulness, for instance, when discussing ultimate boundedness in dynamic systems which guarantees Lyapunov stability. This fact makes the proposed analysis to be potentially useful to investigate global stability properties in dynamic systems in the potential presence of some locally unstable equilibrium points. The results can be applied to stability problems of dynamics systems and circuit theory as the given examples suggest. {\textcopyright} 2013 Elsevier Inc. All rights reserved.",

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AU - De La Sen, M.

AU - Ibeas, A.

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N2 - This paper investigates self-maps T: X → X which satisfy a distance constraint in a metric space with mixed point-dependent non-expansive properties or, in particular, contractive ones, and potentially expansive properties related to some distance threshold. The above mentioned constraint is feasible in certain real-world problems of usefulness, for instance, when discussing ultimate boundedness in dynamic systems which guarantees Lyapunov stability. This fact makes the proposed analysis to be potentially useful to investigate global stability properties in dynamic systems in the potential presence of some locally unstable equilibrium points. The results can be applied to stability problems of dynamics systems and circuit theory as the given examples suggest. © 2013 Elsevier Inc. All rights reserved.

AB - This paper investigates self-maps T: X → X which satisfy a distance constraint in a metric space with mixed point-dependent non-expansive properties or, in particular, contractive ones, and potentially expansive properties related to some distance threshold. The above mentioned constraint is feasible in certain real-world problems of usefulness, for instance, when discussing ultimate boundedness in dynamic systems which guarantees Lyapunov stability. This fact makes the proposed analysis to be potentially useful to investigate global stability properties in dynamic systems in the potential presence of some locally unstable equilibrium points. The results can be applied to stability problems of dynamics systems and circuit theory as the given examples suggest. © 2013 Elsevier Inc. All rights reserved.

KW - Contractive maps

KW - Fixed points

KW - Metric space

KW - Non-expansive maps

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