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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 9.1

A conjecture on Lyapunov equations and

principal angles in subspace identification

Katrien De Cock and Bart De Moor1

Dept. of Electrical Engineering (ESAT–SCD)

K.U.Leuven

Kasteelpark Arenberg 10

B-3001 Leuven

Belgium

http://www.esat.kuleuven.ac.be/sista-cosic-docarch

decock@esat.kuleuven.ac.be,demoor@esat.kuleuven.ac.be

1 DESCRIPTION OF THE PROBLEM

The following conjecture relates the eigenvalues of certain matrices that are derived from the solution of a Lyapunov equation that occurred in the analysis of stochastic subspace identification algorithms [3]. First, we formulate the conjecture as a pure matrix algebraic problem. In Section 2, we will describe its system theoretic consequences and interpretation.

Lyapunov equation

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