descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 2015Publisher:EDP SciencesJournal:ESAIM: Proceedings and Surveys, volume 49, pages 23-36 (eissn: 2267-3059,

Authors: Bernoussi A.; Bel Fekih A.;

doi: 10.1051/proc/201549003

Regional Stability and Stability Radius

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Abstract

Summary: In this work, we consider the problem of stability, for distributed parameter systems, through the space variable. We give an extension of the stability radius, introduced by \textit{A. J. Pritchard}, \textit{S. Townley} [''Robustness of linear systems'', J. Differ. Equations 77, No.2, 254-286 (1989; Zbl 0674.34061)], \textit{D. ~Hinrichsen}, \textit{A.~J.~ Pritchard} [''Stability radii of linear systems'', Syst. Control Lett. 7, 1-10 (1986; Zbl 0631.93064)] to the regional case. This consists to determine the ``smallest disturbance'' which destabilizes regionally an exponentially stable system. We prove in particular that for a certain given class of distributed parameter systems, it is possible to destabilize regionally an exponential stable system without destabilizing it totally.

Keywords

Asymptotic stability in control theory, destabilization regionally an exponentially stable system, T57-57.97, Applied mathematics. Quantitative methods, Perturbations in control/observation systems, QA1-939, stability radius, regional stability, Mathematics

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