Communications in Information and Systems

Volume 8 (2008)

Number 4

Infinite-Dimensional Feedback Systems: the Circle Criterion and Input-to-State Stability

Pages: 413 – 444



Bayu Jayawardhana

Hartmut Logemann

Eugene P. Ryan


An input-to-state stability theory, which subsumes results of circle criterion type, is developed in the context of a class of infinite-dimensional systems. The generic system is of Lur'e type: a feedback interconnection of a well-posed infinite-dimensional linear system and a nonlinearity. The class of nonlinearities is subject to a (generalized) sector condition and contains, as particular subclasses, both static nonlinearities and hysteresis operators of Preisach type.


Absolute stability; circle criterion; hysteresis; input-to-state stability; well-posed infinite-dimensional systems

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