Global and local stability properties of a non-SPR output error estimator

Conditions for local instability are compared with conditions for global asymptotic stability of an output error adaptive estimation algorithm for continuous-time systems. A boundedness conjecture is made that all signals within this adaptive system including the output error and parameter estimates...

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Bibliographic Details
Published in:International journal of control 1989-09, Vol.50 (3), p.937-953
Main Authors: SCHOENWALD, DAVID A., KOKOTOVIC, PETAR V.
Format: Article
Language:English
Subjects:
Adaptative systems
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
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Summary:Conditions for local instability are compared with conditions for global asymptotic stability of an output error adaptive estimation algorithm for continuous-time systems. A boundedness conjecture is made that all signals within this adaptive system including the output error and parameter estimates remain globally bounded for all time despite any locally unstable behaviour. A global stability criterion applied to a transfer function, which is not strictly positive real, states that for a large enough adaptation gain the system will be asymptotically stable. However, a local result states that for a small enough adaptation gain the same system is unstable. The results suggested by the computer simulations are verified by an exact analysis of a linearized periodic version of the adaptive system.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207178908953408