Zeros of Multivariable Systems: Definitions and Algorithms.
Abstract
A number of definitions of zeros of linear time-invariant multivariable systems have appeared recently. This work surveys selected literature on these zeros. Two questions are addressed here. First, how are zeros defined and how are these definitions interrelated. Second, how can they be calculated. The definitions of zeros are considered for three system representations: (1) the transfer function matrix, (2) the state space representation in the frequency domain, and (3) the state space representation in the time domain. The definitions of zeros for transfer function matrices are shown to be (mostly) equivalent. However, several different sets of zeros are defined for state space representations. The interrelationships between all of these definitions is discussed in detail. It turns out that the calculation of zeros directly from the definitions is not always tractable. The properties of zeros, however, provide several algorithms for calculating zeros. Finally, a new algorithm for the calculation of invariant zeros is introduced. It is based on the geometrical properties of linear time invariant systems. This algorithm is applicable to the most general class of systems (A,B,C,D).
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1979
- Accession Number
- ADA077147
Entities
People
- Douglas Kent Lindner
Organizations
- University of Illinois Urbana–Champaign