Title :
Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem
Author_Institution :
Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA
fDate :
7/1/1998 12:00:00 AM
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 :
asymptotic stability; delay systems; differential equations; multidimensional systems; nonlinear control systems; Razumikhin-type theorems; asymptotic stability; delay systems; finite-dimensional systems; functional differential equations; input-to-state stability; nonlinear control systems; nonlinear small-gain theorem; Asymptotic stability; Control systems; Delay effects; Delay systems; Difference equations; Differential equations; Lyapunov method; Nonlinear control systems; Robust control; Typesetting;
Journal_Title :
Automatic Control, IEEE Transactions on
