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Polynomial Matrix Descriptions and Matrix Fractional Descriptions of Systems

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Linear Systems

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7.5 Summary

In this chapter alternatives to state-space descriptions were introduced and used to further study the behavior of linear time-invariant systems and to study in depth structural properties of feedback control systems.

In Part 1, the properties of systems described by Polynomial Matrix Descriptions (PMDs) were explored in Section 7.3 and background on polynomial matrices was provided in Section 7.2. The Diophantine Equation, which plays an important role in feedback systems, was studied at length in Subsection 7.2E.

An in-depth study of the theory of parameterizations of all stabilizing controllers with emphasis on PMDs was undertaken in Part 2, Subsection 7.4A, and the parameterizations of all proper stabilizing controllers in terms of proper and stable Matrix Fraction Descriptions (MFDs) were derived in Subsection 7.4C. State feedback and state estimation using PMDs were studied in Subsection 7.4B. Finally, control systems with two degrees of freedom controllers were explored in Subsection 7.4D, with an emphasis on stability, parameterizations of all stabilizing controllers, and attainable response maps.

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© 2006 Birkhäuser Boston

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(2006). Polynomial Matrix Descriptions and Matrix Fractional Descriptions of Systems. In: Linear Systems. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4435-0_7

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  • DOI: https://doi.org/10.1007/0-8176-4435-0_7

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-4434-5

  • Online ISBN: 978-0-8176-4435-2

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