Stability Radii via Lyapunov Exponents for Large Stochastic Systems

This paper considers nonlinear stochastic systems subject to random Markovian perturbations as the size of the perturbations increases. At an operating point of the system, its exponential stability can be assessed via the Lyapunov exponents. We define an index, the stability radius, which uses the Lyapunov exponents to determine the optimal system parameters for stabilization so that the system can withstand perturbations of maximal magnitude.