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

2006/12/08 by Iasson Karafyllis, Karafyllis, Iasson, Zhong-Ping Jiang +1 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #math.DS #math.OC

paper · pdf · doi:10.48550/arxiv.math/0612210

Submitted for possible publication to SIAM Journal on Control and Optimization

arxiv created 2006/12/08 · arxiv updated 2009/12/01

Abstract

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.

Cited by

• Robust output stability and input-to-output stability based on output dissipation

Related

• An Extended Small-Gain Theorem
• A Small-Gain Theorem with Applications to Input/Output Systems, Incremental Stability, Detectability, and Interconnections
• When Small Gain Meets Small Phase
• A Vector Small-Gain Theorem for General Nonlinear Control Systems
• Small gain theorems for general networks of heterogeneous\n infinite-dimensional systems