**MSC:**- 93D09 Robust stability
- 34D08 Lyapunov exponents

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.