Fabian Wirth
On the calculation of real time-varying stability radii
The paper is published: International Journal of Robust and Nonlinear Control. 8:1043-1058, 1998.
MSC:
93D09 Robust stability
34D08 Lyapunov exponents
Abstract:
The problem of calculating the maximal Lyapunov exponent
(generalized spectral radius) of a discrete inclusion is
formulated as an average yield optimal control problem. It is
shown that the maximal value of this problem can be approximated
by the maximal value of discounted optimal control problems, where
for irreducible inclusions the convergence is linear in the
discount rate. This result is used to obtain convergence rates of
an algorithm for the calculation of time-varying stability radii.


Keywords: Real stability radius, discrete inclusions, generalized spectral radius, Lyapunov exponents, optimal control, discount rates, average yield