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1999

An elementary result in the stability theory of time-invariant nonlinear discrete dynamical systems

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An elementary result in the stability theory of time-invariant nonlinear discrete dynamical systems
The stability of the equilibria of time-invariant nonlinear dynamical systems with discrete time scale is investigated. We present an elementary proof showing that in the case of a stable equilibrium and continuously dierentiable state transition function, all eigenvalues of the Jacobian computed at the equilibrium must be inside or on the unit circle. We also demonstrate via numerical examples that if some eigenvalues are on the unit circle and all other eigenvalues are inside the unit circle, then the equilibrium maybe unstable, or marginally stable, or even asymptotically stable, which show that the necessary condition cannot be further restricted in general. In addition, the necessary condition is given in terms of spectral radius and matrix norms.
Weiye Li, Ferenc Szidarovszky
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1999
Where AMC
Authors Weiye Li, Ferenc Szidarovszky
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