The stability and instability of partial realizations

✍ Scribed by Christopher I. Byrnes; Anders Lindquist

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 533 KB
• Volume: 2
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(82)80018-2

✦ Synopsis

A finite or infinite sequence of real numbers is said to be stable if it admits minimal realization by a stable linear system. It is shown that the preservation of stability as such a sequence is truncated or extended is not a generic property even among stable sequences. This is of interest for identification of linear systems from partial data and for partial realization of random systems, in which cases it constitutes a negative result. Certain finite sequences have infinitely many minimal realizations each having different stability properties.

In this case, a graphical criterion in the spirit of the Nyquist criterion is derived to exploit this lack of uniqueness in order to determine whether one can achieve a stable pole placement by a judicious choice of partial realization.