4. Block Hessenberg Forms
Given the state-space realization
of a linear system, numerically stable methods to obtain canonical realizations of the system are desirable. For this purpose, Advanced Numerical Methods provides the four new functions: ControllerHessenbergForm, ObserverHessenbergForm, LowerControllerHessenbergForm, and UpperObserverHessenbergForm. The transforming matrices for these realizations are orthogonal matrices and are, thus, well-conditioned. In contrast, the transforming matrices that transform the state-space systems to the controller and observer canonical forms can be extremely ill-conditioned.
In Control System Professional, the controllability and observability of a system are tested by using the functions Controllable and Observable, respectively. Two new options, FullRankControllerHessenbergBlocks and FullRankObserverHessenbergBlocks, are introduced in Advanced Numerical Methods to use with these functions.