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Small-gain theorem for ISS systems and applications. (English) Zbl 0836.93054
A concept of input-to-output practical stability of smooth nonlinear control systems is introduced. A generalized small-gain theorem and a gain assignment theorem are proved. Applications are obtained:
– A sufficient condition for global asymptotic stability (in the spirit of the center manifold reduction theorem);
– Sufficient conditions for global asymptotic stabilization (via partial-state feedback) for linear systems with nonlinear stable dynamic perturbations and for a class of nonlinear control systems composed of a chain of dynamically perturbed integrators.

MSC:
93D25 Input-output approaches in control theory
93D15 Stabilization of systems by feedback
93D20 Asymptotic stability in control theory
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