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We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series...

Popov criterion Integral control Circle criterion Infinite-dimensional systems Discrete-time systems Nonlinear Volterra difference equations Absolute stability

We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series...

Popov criterion Integral control Circle criterion Infinite-dimensional systems Discrete-time systems Nonlinear Volterra difference equations Absolute stability

An input-to-state stability theory, which subsumes results of circle criterion type, is developed in the context of continuous-time Lur’e systems. The approach developed is inspired by the complexified Aizerman conjecture.

Absolute stability Circle criterion Complexified Aizerman conjecture Input-to-state stability Lur’e systems Stability radius

An input-to-state stability theory, which subsumes results of circle criterion type, is developed in the context of continuous-time Lur’e systems. The approach developed is inspired by the complexified Aizerman conjecture.

Absolute stability Circle criterion Complexified Aizerman conjecture Input-to-state stability Lur’e systems Stability radius