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Kurt J. Reinschke, Oliver Fritsche

Geometric Approach to Pole Assignability by Means of Static Output Feedback

This contribution deals with arbitrary pole assignability by means of static output feedback for linear time-invariant MIMO systems. The application of tools from algebraic geometry allows to derive conditions of arbitrary pole assignability. Each admissible static feedback law may be interpreted as a point at a Grassmannian manifold within a projective space. Assuming the number of scalar inputs multiplied by the number of scalar outputs to be greater than the dynamic order of the plant, a necessary and a sufficient condition of arbitrary pole assignability are formulated and proved. The authors present a procedure for determining a static output feedback matrix by means of which the desired pole placement is achieved. A nontrivial example system is treated to completely illustrate the individual steps of the procedure.

at – Automatisierungstechnik, Oldenbourg Wissenschaftsverlag

Print ISSN: 0178-2312
Volume: 52, 09/2004
Pages: 432 - 439

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