Note: This content is accessible to all versions of every browser. However, this browser does not seem to support current Web standards, preventing the display of our site's design details.


A Theorem of the Alternative for the Existence of a Lyapunov Function


H. Peyrl

IfA Internal Seminar Series

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, global stability of an equilibrium point is proved. In practice one only considers functions of a certain class (e.g., polynomials) and parameterizes the candidate function accordingly. The problem is then posed as a feasibility problem: if it is feasible, stability has been proved. However, if the problem is infeasible, no firm conclusion about stability can be drawn. 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. Elements in the dual space have a natural interpretation in terms of occupation measures of system trajectories and can be used to provide a certificate of infeasibilty of the Lyapunov stability problem.


Type of Publication:


No Files for download available.
% No recipe for automatically generating a BibTex entry for (06)Talk
Permanent link