Linear Analysis

  • Geir E. Dullerud
  • Fernando Paganini
Chapter
Part of the Texts in Applied Mathematics book series (TAM, volume 36)

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.

Keywords

Hilbert Space Normed Space Product Space Spectral Radius Banach Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Geir E. Dullerud
    • 1
  • Fernando Paganini
    • 2
  1. 1.Department of Mechanical and Industrial EngineeringUniversity of IllinoisUrbanaUSA
  2. 2.Department of Electrical EngineeringUniversity of CaliforniaLos AngelesUSA

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