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Scalar control of linear multivariable systems over C[y]: A symmetric approach
Abstract
The by now classical but still unsolved problem of the existence of a scalar control for multivariable linear systems with complex polynomial coefficients is transformed to an almost symmetric equivalent problem, which is remarkably easier and actually leads to a solution up to dimension four, for the moment
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Based on an “almost”-control-canonical form for reachable systems over PIDs, it is shown that coefficient assignment is possible over K[y], where K is an algebraically closed field of arbitrary characteristic. As consequences, the ring of polynomials C[y] over the complex numbers is a CA-ring, and there are (PID) CA-rings that are not FC-rings.
Given a square n-matrix F and an n-row matrix G, pole-shifting problems consist in obtaining more or less arbitrary characteristic polynomials for F+GK, for suitable (“feedback”) matrices K. A review of known facts is given, various partial results are proved, and the case n = 2 is studied in some detail.
This paper answers in the affirmative the following open question for 3-dimensional linear systems over the ring of complex polynomials in one variable: “If the system is reachable, does there exist a feedback that makes it reachable from a single input channel?” The result given remains valid for slightly more general coefficient domains.
Normalformenproblem und Koef-fizientenzuweisung bei Systemen uber Ringen, Diplom-arbeit
- J Dubbelde
J. Dubbelde, Normalformenproblem und Koef-fizientenzuweisung bei Systemen uber Ringen, Diplom-arbeit, Universitat Oldenburg, 1994.
Normalformenproblem und Koeffizientenzuweisung bei Systemen über Ringen
- J Dübbelde