LQG balancing: Intertwining balancing and sign iterations

In this paper an efficient new approach to LQG balancing is presented. We propose an algorithm which intertwines iterations of a matrix sign function computation with state space balancing iterations, giving directly the balancing transformation upon convergence. Our approach has the advantage that the balancing and sign iterations can be computed in parallel and therefore can yield a performance gain in a suitable parallel implementation. In particular, our approach does not require as a first step the solution of the control and filter Riccati equations followed by the second step of calculating the balancing transformation from the solutions.