3,063 research outputs found
A complete characterization of exponential stability for discrete dynamics
For a discrete dynamics defined by a sequence of bounded and not necessarily
invertible linear operators, we give a complete characterization of exponential
stability in terms of invertibility of a certain operator acting on suitable
Banach sequence spaces. We connect the invertibility of this operator to the
existence of a particular type of admissible exponents. For the bounded orbits,
exponential stability results from a spectral property. Some adequate examples
are presented to emphasize some significant qualitative differences between
uniform and nonuniform behavior.Comment: The final version will be published in Journal of Difference
Equations and Application
Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes
In this paper we show that uniformly global asymptotic stability for a family
of ordinary differential equations is equivalent to uniformly global
exponential stability under a suitable nonlinear change of variables. The same
is shown for input-to-state stability and input-to-state exponential stability,
and for input-to-state exponential stability and a nonlinear
estimate.Comment: 14 pages, several references added, remarks section added, clarified
constructio
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