Fading memory and necessity of the small gain theorem

Jeff S. Shamma*, Rongze Zhao

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

The authors consider fading memory for nonlinear time-varying systems and associated problems of robust stability. They establish notation, state some preliminary results, and consider the fading memory property. Uniform and pointwise fading memory are defined. The focus is on the differences between pointwise and uniform fading memory, and conditions are provided for an operator to have pointwise fading memory. Previous results showing that the small-gain theorem is necessary for robust stability of fading memory nonlinear systems are generalized. These results are applied to a robust stabilization problem. Conditions are presented under which a closed-loop system exhibits fading memory.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherPubl by IEEE
Pages788-793
Number of pages6
ISBN (Print)0780304500
StatePublished - Jan 1 1992
EventProceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) - Brighton, Engl
Duration: Dec 11 1991Dec 13 1991

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

OtherProceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)
CityBrighton, Engl
Period12/11/9112/13/91

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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