Computing time-varying stability radii via discounted optimal control

The problem of calculating the maximal Lyapunov exponent of a discrete inclusion (or equivalently its generalized spectral radius) 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