Transmission zeroes

A transmission zero is a frequency at which the transfer function of a linear two-port network has zero transmission. Transmission zeroes at zero frequency and infinite frequency may be found in high-pass filters and low-pass filters respectively. Transmission zeroes at finite, non-zero frequency may be found in Band-stop filters, elliptic filters, and Type II Chebyshev filters. Transfer functions with both zero and infinite frequency can be found in band-pass filters. A transfer function may have multiple zeroes at the same frequency. A transfer function may have any number of transmission zeroes at zero frequency and infinite frequency, but transmission zeroes at finite non-zero frequency always come in conjugate pairs

Dear Biswajit,

in the transfer function matrix of a MIMO system, the roots of each numerator as they have a common denominator are known as the element zero.

the transmission zero is related to the frequencies in which the transmission between inputs-outputs are blocked. Such zero(s) can be obtained by finding a special representation of transfer function, which is known as the Smith-MacMillan.

it is explained in this book very well , see:

J.M. Maciejowski, Multivariable Feedback Design, Addison-Wesley Pub, 1st printed 1989 edition.

element zeros have no effects on the non-min phase behaviors and their importance just appears as we are going to design a decentralized control system. In this case, they could have great effects on the stability of decentralized closed loop system, for example the effects on "Decentralized Integral Controllability" or DIC conditions of a system.

see:

A. Khaki-Sedigh, B. Moaveni, Control Configuration Selection for Multivariable Plants, Springer, 2009.