The output zeroing problem and its relationship to the invariant zero structure : a matrix pencil approach

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Abstract
Multivariable zeros have boon defined in a multitude of ways and of these the physical definition of zeros through the problem of zeroing outputs is preferred here. The extension of this definition, from the external to the internal description undertaken, proves the zeros with the corresponding zero directions to be dual concepts to the poles and corresponding modes. The treatment, adopted in this paper leads to the definition of the zero pencil, Z(s) which through the theory of matrix pencils, proves to be an effective means for the analysis of the zero system structure. Use of the Kroneeker canonical form of Z(s) enables the zero properties of the system to be related to the geometric theory of Wonham and Morse. A practical application of the results concerning the placement of zeros brings the paper to a conclusion.