GEOMETRIC APPROACH TO ANALYSIS AND SYNTHESIS OF SYSTEM ZEROS - 1, 2.

Journal article

The concepts of poles and zeros of a matrix-valued function of a complex variable form a natural link between frequency-response and state-space approaches to the multivariable feedback problem. For square matrix-valued functions of a complex variable a method is given for computing the invariant zeros in terms of the parameters of the corresponding state-space model. The analysis presented gives an interesting insight into the geometrical relationships which underly the concept of invariant zeros. An algorithm is derived which should be useful for the direct calculation of zeros from state-space descriptions. A method is derived for computing the invariant zeros of a general non-square matrix-valued function of a complex variable in terms of the parameters of the corresponding state-space system model. Based on this a method is developed for choosing a ″squaring down″ output matrix to give a desired set of zero locations for a system whose states are all accessible. This technique is then extended to deal with the situation when all the states are not accessible.

Authors: Kouvaritakis, B; MacFarlane, A

• Journal: International Journal of Control
• Volume: 23
• Issue: 2
• Pages: 149-181
• Publication date: 1976-02-01
• ISSN: 0020-7179