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Informal Systems Seminar (ISS), Centre for Intelligent Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisions (GERAD)

On Bounded Solutions of Linear SDEs Driven by Convergent System Matrix Processes with Hurwitz Limits*

David Levanony
Department of Electrical and Computer Engineering Ben Gurion University

October 11, 2019 at  11:00 AM
McConnell Engineering Room 437

Linear time-varying stochastic differential equations with a.s. continuous, convergent random system matrix processes are considered. We show that given the limit is known to be Hurwitz (i.e. asymptotically stable), the generated state solutions are a.s. bounded. This property is shown to hold by substantiating that, w.p.1, (i) no finite escape time exists and (ii) no divergence to infinity, as t goes to infinity, may occur. We end with an adaptive control application example.
* Based on a joint work with Peter E. Caines