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Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Spring 2008 Seminar Series
Presents
An Asymptotic Analysis of Random Lyapunov and
Riccati Recursions
Babak Hassibi
California Institute of Technology
Friday, May 16, 2008 3:00-4:00pm Harold Frank Hall 1104
Abstract:
Lyapunov and Riccati recursions frequently arise in estimation and control. In adaptive filtering,
as well as in problems of distributed estimation and control over lossy networks, the resulting
recursions have coefficient matrices that are drawn randomly from some distribution. In such
situations the solution to the recursions form a matrix-valued random process, which makes
the stability and convergence analysis (which is necessary to evaluate the performance of the
underlying estimators and controllers) quite challenging. Motivated by recent results in large
random matrix theory, in particular the transform techniques pioneered by Marcenko and Pas-
tur, we present a general approach to studying the asymptotic eigen distribution of the solu-
tion to random Lyapunov and Riccati recursions. In quite a few cases the approach provides a
complete solution, whereas in others there remain open issues. This talk will provide a survey
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