A singular perturbation model of reliability in systems control

In many engineering systems, the intensity of the input noise is small and the state trajectory is mainly due to the deterministic part of the system structure. When this is the case for a white input noise, the mean exit-time from the reliability region may be represented as a solution to a partial differential equation with a small parameter multiplying the highest derivatives. Hence, the evaluation of the mean exit-time from the reliability region reduces to the solution of a singularly perturbed partial differential equation for which an asymptotic solution can be evaluated analytically in a fairly general case. The mean exit-time is then used to measure the reliability of some decentralized control policies for linear stochastic systems.