Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem
- 1 July 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 43 (7) , 960-964
- https://doi.org/10.1109/9.701099
Abstract
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.Keywords
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