Second-Moment Stability Boundaries for LTI SDDEs

This talk describes the derivation of optimal, semi-analytic, algebraic equality conditions that can be used to identify second-moment stability boundaries in linear, time-invariant stochastic delay-differential equations with a single constant delay and both multiplicative and additive noise, without the use of problem discretization. As illustrated for applications in robot control and machine tool vibrations, such boundaries define critical parameter combinations beyond which the accumulated influence of noise results in local exponential growth of variance even before any instability is visible in the mean. The predictions of closed-form analysis and numerical parameter continuation are successfully validated against Monte Carlo simulations and published results for several low-dimensional models, helping to clarify limitations of stability conditions proposed in the literature and demonstrating considerable savings in computational effort relative to discretization-based approaches.