[Ian, Lee]

Balancing state space systems is essential for getting the RMS plots correct for the comparison of controllers. When using the solution for the Lyapunov equation the solver benefits greatly. Adding the wrapped version of Slycot's AB09ND was the key to getting the H2 Lyapunov solver to correctly display the shape of the RMS H2 optimal curve. AB09ND "compute[s] a reduced order model (Ar,Br,Cr,Dr) for an original state-space representation (A,B,C,D) by using either the square-root or the balancing-free square-root Singular Perturbation Approximation (SPA) model reduction method for the ALPHA-stable part of the system" (from documentation).

Another way that was shown to be effective at helping the Laub method to work in some updates for GWINC is the TB01ID. We were wondering if this would be as effective on our code given that AB09ND is calling TB01ID. We ran the code with balancing from AB09ND, balancing from TB01ID, and no balancing.

We found that the only balancing option that gave us a segment of continuous RMS gradient was AB09ND. Both TB01ID and the no balancing showed a scatter which should not be the case.

We have attached the RMS plots for all three situations.