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Article overview
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Exponential Stability and the Markus-Yamabe Conjecture in Compact Spaces | Ravi Mazumdar
; Christopher Nielsen
; Arpan Mukhopadhyay
; | Date: |
2 Sep 2016 | Abstract: | In this note we show that if a continuous-time, nonlinear, time-invariant,
finite-dimensional system evolves on a compact subset of Rn and if the Jacobian
of the vector field is Hurwitz at each point of the compact set, then there is
a unique equilibrium on the set and solutions exponentially converge to it.
This shows that the Markus-Yamabe conjecture, which is false in general on Rn,
n>2, holds on compact sets. The results of this note can be viewed as an
application of Krasovskii’s method for constructing Lyapunov functions and we
are able to similarly construct Lyapunov-like functions valid on the given
compact set. Examples are provided to illustrate the result. | Source: | arXiv, 1608.8657 | Services: | Forum | Review | PDF | Favorites |
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