The Block form of Linear Systems over Commutative Rings with Applications to Control

  • Edward W. Kamen
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 62)


This paper deals with a new approach to the study of linear time-invariant discrete-time systems whose coefficients belong to an arbitrary commutative ring. Such systems arise in the study of integer systems, systems depending on parameters, and multi-dimensional systems. The key idea is to consider the representation of systems over a ring in terms of a block-input/block-output form. By time-compressing the block representation, new results are derived on assignability by state feedback control including the construction of deadbeat controllers. A new type of state observer is then considered based on a block-output form for the update term in the state estimate. The results on state observers are combined with the time-compression approach to state feedback control to yield a new type of input/output regulator. In the last section of the paper the results are applied to the problem of state and output tracking of set points.

Key words

Systems over rings reachability observability feedback control observers regulators tracking 

AMS(MOS) subject classifications

93B05 93B07 93B25 93C05 93C45 93C55 93D15 


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Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Edward W. Kamen
    • 1
  1. 1.School of Electrical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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