You are here : Control System Design  Index  Book Contents  Appendix B  Section B.5 B. Smith McMillan FormsB.5 Poles and ZerosThe SmithMcMillan form can be utilized to give an unequivocal definition of poles and zeros in the multivariable case. In particular, we have:
Definition B.11
Consider a transferfunction matrix ,
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In the case of square plants (same number of inputs as outputs), it follows that is a simple function of and . Specifically, we have
Note, however, that and are not necessarily coprime. Hence, the scalar rational function is not sufficient to determine all zeros and poles of . However, the relative degree of is equal to the difference between the number of poles and the number of zeros of the MIMO transferfunction matrix.
