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Published December 2008 | Published
Book Section - Chapter Open

A Stieltjes transform approach for studying the steady-state behavior of random Lyapunov and Riccati recursions

Abstract

In this paper we study the asymptotic eigenvalue distribution of certain random Lyapunov and Riccati recursions that arise in signal processing and control. The analysis of such recursions has remained elusive when the system and/or covariance matrices are random. Here we use transform techniques (such as the Stieltjes transform and free probability) that have gained popularity in the study of large random matrices. While we have not yet developed a full theory, we do obtain explicit formula for the asymptotic eigendistribution of certain classes of Lyapunov and Riccati recursions, which well match simulation results. Generalizing the results to arbitrary classes of such recursions is currently under investigation.

Additional Information

© 2008 IEEE. This work was supported in part by the National Science Foundation under grant CCF-0729203, by the David and Lucille Packard Foundation, and by Caltech's Lee Center for Advanced Networking.

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Additional details

Created:
August 20, 2023
Modified:
March 5, 2024