Maximum Lyapunov exponents and stability criteria of linear systems with variable delay

Maximum Lyapunov exponents and stability criteria of linear systems with variable delay

The Myshkis problem of the maximum Lyapunov exponent of a first-order linear differential equation with an arbitrary bounded delay is solved. The result obtained is generalized to a system of equations of arbitrary order, whose matrix has real eigenvalues. A sufficient condition for exponential stab...

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Veröffentlicht in:Journal of applied mathematics and mechanics 2015-01, Vol.79 (1), p.1-8
1. Verfasser: Zevin, A.A.
Format: Artikel
Sprache:eng
Schlagworte:
Criteria
Delay
Differential equations
Eigenvalues
Linear systems
Lyapunov exponents
Mathematical analysis
Stability
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Beschreibung
Zusammenfassung:The Myshkis problem of the maximum Lyapunov exponent of a first-order linear differential equation with an arbitrary bounded delay is solved. The result obtained is generalized to a system of equations of arbitrary order, whose matrix has real eigenvalues. A sufficient condition for exponential stability is obtained for a system with complex eigenvalues.
ISSN:0021-8928
0021-8928
DOI:10.1016/j.jappmathmech.2015.04.011