Title :
A Stieltjes transform approach for studying the steady-state behavior of random Lyapunov and Riccati recursions
Author :
Vakili, Ali ; Hassibi, Babak
Author_Institution :
Electr. Eng. Dept., California Inst. of Technol., Pasadena, CA, USA
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.
Keywords :
Lyapunov methods; Riccati equations; covariance matrices; eigenvalues and eigenfunctions; Riccati recursions; Stieltjes transform; asymptotic eigenvalue distribution; covariance matrices; random Lyapunov steady-state behavior; time-invariant Lyapunov; Control system analysis; Convergence; Covariance matrix; Eigenvalues and eigenfunctions; Process control; Random processes; Riccati equations; Signal processing; Steady-state; Time varying systems;
Conference_Titel :
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on
Conference_Location :
Cancun
Print_ISBN :
978-1-4244-3123-6
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2008.4739258