A Small-Gain Theorem for a Wide Class of Feedback Systems with Control Applications

Details A Small-Gain Theorem for a Wide Class of Feedback Systems with Control Applications A Small-Gain Theorem for a Wide Class of Feedback Systems with Control Applications

2006-12-08

arxiv.org/abs/math/0612210v1

Mathematics

Optimization and Control

Submitted for possible publication to SIAM Journal on Control and Optimization

Scientific paper

A Small-Gain Theorem, which can be applied to a wide class of systems that includes systems satisfying the weak semigroup property, is presented in the present work. The result generalizes all existing results in the literature and exploits notions of weighted, uniform and non-uniform Input-to-Output Stability (IOS) property. Applications to partial state feedback stabilization problems with sampled-data feedback applied with zero order hold and positive sampling rate, are also presented.

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