7. Model Reduction
The Control System Professional function InternallyBalancedForm finds an internally balanced realization of a stable, controllable, and observable system. From this balanced realization, the function DominantSubsystem extracts the dominant subsystem, corresponding to the large modes, which is then used as a reduced-order model. Advanced Numerical Methods introduces two more numerical methods (the Schur method and the square-root method) for model reduction that can be used as an option for the function DominantSubsystem. Furthermore, Advanced Numerical Methods contains two new functions with CholeskyFactorControllabilityGramian and CholeskyFactorObservabilityGramian that compute, respectively, the Cholesky factors of the controllability and observability Gramian of a stable system. These functions are used to implement the new methods for model reduction and to compute the Hankel singular values of a stable system.