Diagonal stability of stochastic systems subject to nonlinear disturbances and diagonal H2 norms

A known result in the stability theory of stochastic systems with nonlinear Lipschitz-bounded noise intensity states that the robust stability radius of such a stochastic system is equal to the inverse of the H₂ norm of its `noise-to-output´ transfer function. This paper extends this result to the case where one is interested in the diagonal stability of the system under consideration. This problem arises naturally when studying large-scale interconnected systems subject to random perturbations, as one is often interested in using diagonal or block-diagonal Lyapunov functions for such plants. The main result of the paper is the characterization of the diagonal stochastic stability radius, which is similar to the mentioned result for non-diagonal stability.