scholarly journals Exponential stability of boundary controlled port Hamiltonian systems with dynamic feedback

2013 ◽  
Vol 46 (26) ◽  
pp. 115-120
Author(s):  
Hector Ramirez ◽  
Hans Zwart ◽  
Yann Le Gorrec
Keyword(s):  
Exponential Stability ◽  
Hamiltonian Systems ◽  
Dynamic Feedback

scholarly journals Generic super-exponential stability of invariant tori in Hamiltonian systems

2010 ◽  
Vol 31 (5) ◽  
pp. 1287-1303 ◽  
Author(s):  
ABED BOUNEMOURA
Keyword(s):  
Hamiltonian System ◽  
Exponential Stability ◽  
Fixed Points ◽  
Hamiltonian Systems ◽  
Normal Forms ◽  
Invariant Tori ◽  
The Other ◽  
New Method ◽  
Stable Invariant

AbstractIn this article, we consider solutions that start close to some linearly stable invariant tori in an analytic Hamiltonian system, and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms with a new method for obtaining generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will focus mainly on the neighbourhood of elliptic fixed points, since with our approach the other cases can be treated in a very similar way.

scholarly journals Exponential Stabilization of Boundary Controlled Port-Hamiltonian Systems With Dynamic Feedback

2014 ◽  
Vol 59 (10) ◽  
pp. 2849-2855 ◽  
Author(s):  
Hector Ramirez ◽  
Yann Le Gorrec ◽  
Alessandro Macchelli ◽  
Hans Zwart
Keyword(s):  
Hamiltonian Systems ◽  
Exponential Stabilization ◽  
Dynamic Feedback
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