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On the existence of a Lyapunov function - a dual point of view

Author(s):

H. Peyrl
Conference/Journal:

IfA Internal Seminar Series
Abstract:

Lyapunov's second method is one of the most important cornerstones in the study of stability of dynamical systems. The central ingredient of the approach is the search for a so-called "Lyapunov function", a function of the state that decreases monotonically along trajectories. Once such a function is found, stability of an equilibrium point is proved. The question about the existence of a Lyapunov function may be addressed using duality theory, a well-known concept in functional analysis and convex optimization. Starting with a simple finite state machine as an example, I will show how duality theory is used to derive a theorem of the alternative for the existence of a Lyapunov function. Furthermore, a very natural interpretation of the dual solutions will become apparent. Later on, the presented ideas will be used to motivate a similar result for nonlinear continuous time systems on a compact set.

Year:

2008
Type of Publication:

(06)Talk
Supervisor:



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