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LQR and LQG Designs Using Riccati EquationsBlock Controller-Hessenberg Forms

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.

LQR and LQG Designs Using Riccati EquationsBlock Controller-Hessenberg Forms



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