Title: Multiplicative Noise as a Structured Stochastic Uncertainty Problem
Linear systems with multiplicative, time-varying noise exhibit varied and rich phenomenology. 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.
Bassam Bamieh is Professor of Mechanical Engineering and Associate Director of the Center for Control, Dynamical Systems and Computation (CCDC) at the University of California at Santa Barbara. His research interests are in the fundamentals of Control and Dynamical Systems such as Robust, Optimal and Distributed Control, as well as the applications of systems and feedback techniques in several physical and engineering systems including shear flow transition and turbulence, and the use of feedback in thermoacoustic energy conversion devices. He is a past recipient of the AACC Hugo Schuck Best Paper Award, and the IEEE Control Systems Society G. S. Axelby Outstanding Paper Award (twice). He is a Fellow of the International Federation of Automatic Control (IFAC), and a Fellow of the IEEE.