On the limiting zeros of sampled multivariable systems

✍ Scribed by Yoshikazu Hayakawa; Shigeyuki Hosoe; Masami Ito

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 313 KB
• Volume: 2
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(83)80006-1

✦ Synopsis

For time-invariant linear systems with single input -single output, it has been shown [3] that as the sampling period goes to 0, the zeros of the corresponding discrete time system obtained by sampling converge to some specific constant values determined only be the degrees of the finite and the infinite zeros of the original continuous time system. It is natural to inquire the extent to which this result may be carried over to the case of multivariable systems.

In this note it is shown that the result is true also for muhivariable systems if the difference among the degrees of infinite elementary divisors of the pencil corresponding to the original continuous system is less than two. When the last condition is not satisfied, the limiting values of the zeros of the discrete system depend, in general, not only on the integers cited above but also on system parameters.