Stability of Discrete Time Systems with Stochastically Delayed Feedback

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Marcella M. Gomez, Gabor Orosz and Richard M. Murray
Submitted, 2013 European Control Conference (ECC)

This paper investigates the stability of linear systems with stochastic delay in discrete time. Stability of the mean and second moment of the non-deterministic system is determined by a set of deterministic discrete time equations with distributed delay. A theorem is provided that guarantees convergence of the state with convergence of the second moment, assuming the delays are identically independently distributed. The theorems are applied to a scalar equation where the stability of the equilibrium is determined.