Abstract
Linear systems with multiplicative noise can exhibit sometimes surprising behaviors that are not possible if only additive noise is assumed. This will be demonstrated with very simple low-dimensional examples, as well as examples from large-scale networks where multiplicative noise models stochastically varying network structures. A general framework of structured stochastic uncertainty is developed to obtain necessary and sufficient conditions for mean-square stability from a purely input/output point of view. This framework is applied to study mechanical stability of the dynamics of the mammalian cochlea, which models the “mechanical spectrum analyzer” features of the cochlea, together with an adaptive gain mechanism which is responsible for the large dynamic range of human hearing. This adaptive gain mechanism appears to also be responsible for phenomena such as otoacoustic emissions and possibly Tinnitus, which appear to have mechanical instability origins. We study the structured stochastic uncertainty model of cochlear mechanics, and show the rather small stability margins which are apparently due to the adaptive gain mechanism.
Biography
Bassam Bamieh is Professor of Mechanical Engineering at the University of California at Santa Barbara (UCSB). He received his B.Sc. degree in Electrical Engineering and Physics from Valparaiso University (Valparaiso, IN) in 1983, and his M.Sc. and PhD degrees in Electrical and Computer Engineering from Rice University (Houston, TX) in 1986 and 1992 respectively. Prior to joining UCSB in 1998, he was an Assistant Professor in the Department of Electrical and Computer Engineering and the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign (1991-98).
Professor Bamieh's research interests are in the fundamentals of Controls and Dynamical Systems, as well as the applications of systems and feedback techniques in several physical and engineering systems. These areas include Robust and Optimal Control, distributed and networked control and dynamical systems, shear flow transition and turbulence, quantum control, and the use of feedback in thermoacoustic energy conversion devices. Professor Bamieh has co-authored over 200 refereed publications in Systems and Controls and allied fields. Hi recognitions include the IEEE Control Systems Society G. S. Axelby Outstanding Paper Award (twice), an AACC Hugo Schuck Best Paper Award, and a National Science Foundation CAREER award. He was elected a Distinguished Lecturer of the IEEE Control Systems Society (twice), a Fellow of the International Federation of Automatic Control (IFAC), and a Fellow of the IEEE with the citation “For contributions to robust, sampled-data and distributed control.”
