Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem

A Razumikhin-type theorem that guarantees input-to-state stability for functional differential equations with disturbances is established using the nonlinear small-gain theorem. The result is used to show that input-to-state stabilizability for nonlinear finite-dimensional control systems is robust,...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1998-07, Vol.43 (7), p.960-964
Main Author: Teel, A.R.
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic stability
Computer science
control theory
systems
Control system analysis
Control systems
Control theory. Systems
Delay effects
Delay systems
Difference equations
Differential equations
Exact sciences and technology
Lyapunov method
Nonlinear control systems
Robust control
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Summary:A Razumikhin-type theorem that guarantees input-to-state stability for functional differential equations with disturbances is established using the nonlinear small-gain theorem. The result is used to show that input-to-state stabilizability for nonlinear finite-dimensional control systems is robust, in an appropriate sense, to small time delays at the input. Also, relaxed Razumikhin-type conditions guaranteeing global asymptotic stability for differential difference equations are given.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.701099