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Linear Analysis

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Book cover A Course in Robust Control Theory

Part of the book series: Texts in Applied Mathematics ((TAM,volume 36))

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Abstract

One of the prevailing viewpoints for the study of systems and signals is that in which a dynamical system is viewed as a mapping between input and output functions. This concept underlies most of the basic treatments of signal processing, communications, and control. Although a functional analytic perspective is implicit in this viewpoint, the associated machinery is not commonly applied to the study of dynamical systems. In this course we will see that incorporating more tools from analysis (e.g., function spaces, operators) into this conceptual picture leads to methods of key importance for the study of systems. In particular, operator norms provide a natural way to quantify the “size” of a system, a fundamental requirement for a quantitative theory of system uncertainty and model approximation.

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Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Illinois, 61801, Urbana, IL, USA

    Geir E. Dullerud

  2. Department of Electrical Engineering, University of California, 90095-1594, Los Angeles, CA, USA

    Fernando Paganini

Authors
  1. Geir E. Dullerud
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  2. Fernando Paganini
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© 2000 Springer Science+Business Media New York

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Dullerud, G.E., Paganini, F. (2000). Linear Analysis. In: A Course in Robust Control Theory. Texts in Applied Mathematics, vol 36. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3290-0_4

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  • DOI: https://doi.org/10.1007/978-1-4757-3290-0_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-3189-4

  • Online ISBN: 978-1-4757-3290-0

  • eBook Packages: Springer Book Archive

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