Feedback Stabilization over Commutative Rings with no Right-/Left-Coprime Factorizations

1999/08/17 by Kazuyoshi MORI, MORI, Kazuyoshi
Mathematics · #93A05 #93B50 #93C05 #93C35 #93D15 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:93A05 #msc:93B50 #msc:93C05 #msc:93C35 #msc:93D15

paper · pdf · doi:10.48550/arxiv.math/9908088

7 pages, LaTeX

arxiv created 1999/08/17 · arxiv updated 2009/11/30

Abstract

Anantharam showed in 1985 the existence of a model in which some stabilizable plants do not have its right-/left-coprime factorizations. In this paper, we give a condition of the nonexistence of the right-/left-coprime factorizations of stabilizable plants as a generalization of Anantharam's result. As examples of the models which satisfy the condition, we present two models. We illustrate the construction of a stabilizing controller of stabilizable single-input single-output plants of such models.

Related

• A Parameterization of Stabilizing Controllers over Commutative Rings
• Feedback Stabilization over Commutative Rings: Further study of the coordinate-free approach
• Elementary Factors and Reduced Minors for Linear Systems over Commutative Rings
• Feedback classification of linear systems over von Neumann regular rings
• Relationships Between Necessary Conditions for Feedback Stabilizability