OUTPUT ZEROING PROBLEM AND ITS RELATIONSHIP TO THE INVARIANT ZERO STRUCTURE - MATRIX PENCIL APPROACH

Multivariablc zeros have been defined in a multitude of ways and of these the physical definition of zeros through the problem of zeroing out.pu t.s is preferred here. Tho extension of this defj nit.ion, from the external to t-he internal description undertaken, the zeros with the corresponding 7.01'0 directions to be dual concepts to the poles and corresponding modes. The t.rcaf.mcnt adopted in this papol' leads to the definition of the zero pencil, Z(s) which t lu-ough the theory of matrix pencils, proves to be an effective means for the analysis of the zero system structure. Usc of the Kronecker canonical form of Z(s) enables t.hc zero properties of the system to be related to tho geometric theory of Wonham and Morse. A pract.icnl application of tho results concerning tho placement of zeros bring s tho paper to a conclusion. © 1979 Taylor & Francis Ltd.