Algebraic System Theory, Computer Algebra and Controller Synthesis

Algebraic System Theory, Computer Algebra and Controller Synthesis

Title : Algebraic System Theory, Computer Algebra and Controller Synthesis
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Conference : Conference Honoring Professor Rudolf E. Kalman pp. 355-370
Date: May 01 - May 01, 1990
Journal : Mathematical System Theory: The Influence of R.E. Kalman pp. 355-370
May 01, 1990

Aigebraic system theory as introduced by Kaiman provided a unifying framework for the frequency domain and state-space approaches to linear finite dimensional systems. More significantly it allowed a rapproachement with automata theory which led to the development of extensions to infinite dimensional systems and nonlinear systems. Another important consequence was the popularization of algebraic methods for constructing and analyzing models of systems over arbitrary rings and fields. An important obstac1e for utilizing these powerful mathematical tools in practical applications has been the non availability of emcient and fast algorithms to carry through the precise error-free computations required by these algebraic methods. Recently with the advent of computer algebra this has become possible. In this paper we develop highly emcient, error-free algorithms, for most of the important computations needed in linear systems over fields or rings. We show that the structure of the underlying rings and modules is critical in designing such algorithms. We also discuss the importance of such algorithms for controller synthesis.

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