Differential stability and robust control of nonlinear systems

Tryphon T. Georgiou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper introduces a notion of distance between nonlinear dynamical systems which is suitable for a quantitative description of the robustness of stability in a feedback interconnection. This notion is one of several possible generalizations of the gap metric, and applies to dynamical systems which possess a differential graph. It is shown that any system which is stabilizable by output feedback, in the sense that the closed loop system is input-output incrementally stable and possesses a linearization about any operating trajectory, has a differential graph. A system with a differentiable graph is globally differentiably stabilizable if the linearized model about any bounded input/output trajectory is stabilizable. It is shown that if a nonlinear dynamical system is globally incrementally stabilizable, then it is (globally incrementally) stabilizable by a linear (possibly time-varying) controller. A suitable notion of a minimal opening between nonlinear differential manifolds is introduced and sufficient conditions guaranteeing robustness of stability are provided.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherPubl by IEEE
Pages984-989
Number of pages6
ISBN (Print)0780312988
StatePublished - Dec 1 1993
EventProceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4) - San Antonio, TX, USA
Duration: Dec 15 1993Dec 17 1993

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2
ISSN (Print)0191-2216

Other

OtherProceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4)
CitySan Antonio, TX, USA
Period12/15/9312/17/93

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