On absolute stability
Roger C. McCann (1972)
Annales de l'institut Fourier
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Absolute stability of a compact set is characterized by the cardinality of a fundamental system of positively invariant neighborhoods.
Roger C. McCann (1972)
Annales de l'institut Fourier
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Absolute stability of a compact set is characterized by the cardinality of a fundamental system of positively invariant neighborhoods.
J. Auslander, P. Seibert (1964)
Annales de l'institut Fourier
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Les auteurs étudient la notion de prolongement au sens de T. Ura et ses relations avec la notion d’ensembles positivement invariants. La stabilité au sens de Liapounoff est équivalente à l’invariance par prolongement. Les auteurs dégagent ensuite la notion de “prolongements abstraits” et les notions de stabilité correspondantes; la stabilité absolue (associée au prolongement minimal transitif) et la stabilité asymptotique jouent un rôle important.
Stutson, Donna, Vatsala, A.S. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Lupu, Mircea, Florea, Olivia, Lupu, Ciprian (2009)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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G. K. Kulev, D. D. Bainov (1987)
Collectanea Mathematica
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Andrzej Dzielinski (2005)
International Journal of Applied Mathematics and Computer Science
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This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class...
Venkatesulu, M., Srinivasu, P.D.N. (1992)
Journal of Applied Mathematics and Stochastic Analysis
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J. Iglesias, A. Portela, A. Rovella (2009)
Fundamenta Mathematicae
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A new concept of stability, closely related to that of structural stability, is introduced and applied to the study of C¹ endomorphisms with singularities. A map that is stable in this sense is conjugate to each perturbation that is equivalent to it in a geometric sense. It is shown that this kind of stability implies Axiom A and Ω-stability, and that every critical point is wandering. A partial converse is also shown, providing new examples of C³ structurally stable maps.