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Cancellations in multivariable continuous-time and discrete-time feedback systems treated by greatest common divisor extraction

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2 Author(s)
Desoer, C.A. ; University of California, Berkeley, CA, USA ; Schulman, J.

This correspondence considers a multivariable system with proper rational matrix transfer functions G0and Gfin the forward and feedback branches, respectively. It develops a strictly algebraic procedure to obtain polynomials whose zeros are the poles of the matrix transfer functions from input to output (Hy), and from input to error (He). G0and Gfare given in the polynomial matrix factored form N_{0}D_{0}^{-1} and D_{f}^{-1}N_{f} . The role of the assumption det [ I + G_{f}(\infty )G_{0}(\infty )] \neq 0 and the relation between the zeros of det [ I + G_{f}G_{0} ] and the poles of Hyand Heare indicated. The implications for stability analysis of continuous-time as well as discrete-time systems are stressed.

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Automatic Control, IEEE Transactions on  (Volume:18 ,  Issue: 4 )