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Babak Hassibi
California Institute of Technology
Title: Asymptotic Eigenanalysis of Large Random Lyapunov and Riccati Recursions
Abstract: Random Lyapunov and Riccati recursions, i.e., recursions with random coefficient matrices drawn from a certain distribution, arise frequently in problems of estimation and control over lossy networks, and in adaptive filtering and control. Unfortunately, they are not very amenable to analysis using current techniques and the best available are (normally loose) upper and lower bounds. In this talk, I will leverage methods from the theory of large random matrices, especially transform techniques, to develop a framework to study the asymptotic (in time) eigendistribution of random Lyapunov and Riccati recursions for systems with a large number of states. While we have not been able to solve the problem in its full generality, we do find explicit expressions for the eigendistribution in many important cases of interest which exhibit excellent agreement with numerical simulations for systems with as low as 10 states. The results are new both in the context of estimation and control, as well as random matrix theory. I will also discuss various implications as well as some open problems.