Logarithmic integrals and system dynamics

An analogue of Bode's sensitivity integral for continuous-time, time-varying systems

Research output: Contribution to journalArticle

Abstract

A new time-domain interpretation of Bode's integral is presented. This allows for a generalization to the class of time-varying systems which possess an exponential dichotomy. It is shown that the sensitivity function is constrained, on average, by the spectral values in the dichotomy spectrum of the antistable component of the open-loop dynamics.

Original languageEnglish (US)
Pages (from-to)451-471
Number of pages21
JournalLinear Algebra and Its Applications
Volume343
DOIs
StatePublished - Mar 1 2002

Fingerprint

Logarithmic integral
Exponential Dichotomy
Time-varying Systems
Time varying systems
Dichotomy
System Dynamics
Continuous Time
Time Domain
Dynamical systems
Analogue
Interpretation
Generalization
Class

Keywords

  • Exponential dichotomies
  • Inner/outer factorizations
  • Sensitivity
  • Time-varying systems

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Numerical Analysis

Cite this

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abstract = "A new time-domain interpretation of Bode's integral is presented. This allows for a generalization to the class of time-varying systems which possess an exponential dichotomy. It is shown that the sensitivity function is constrained, on average, by the spectral values in the dichotomy spectrum of the antistable component of the open-loop dynamics.",
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