Chapter of CSS/CASS/SMCS Presents
DATE: April 27, 2021
TIME: 7:00-8:00 PM ET
TOPIC: MULTIPLICATIVE NOISE AS A STRUCTURED STOCHASTIC UNCERTAINTY PROBLEM
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Linear systems with multiplicative, time-varying noise exhibit varied and rich phenomenology such as heavy tails and dramatic differences between different notions of convergence. We study such systems in a framework similar to that used in robust control where the stochastic parameters are viewed as a "structured uncertainty". In particular, a purely input-output approach is developed to characterize mean-square stability. This approach clarifies earlier results in this area and also easily produces new ones in the case of correlated uncertainties. Applications of this framework to networked dynamical systems with link failures and stochastic topologies will be illustrated. In addition, an application to a model of the Cochlea will be described which potentially explains otoacoustic emissions as an instability mechanism. Finally, we illustrate some interesting connections of this work with the phenomenon of Anderson Localization which is a canonical problem in the statistical physics of disordered media.