Abstract
We study absolute stability of a class of discrete Lur'e control system on an infinite-dimensional Hilbert space. Counterparts of the circle criterion and the Szegö criterion are derived using, respectively, quadratic and non-quadratic Lyapunov functionals. A link with existing finite-dimensional theory of absolute stability is shown. The results are illustrated by an example of the loaded distortionless electric RLCG-transmission line with a nonlinear static feedback. Its stability was previously investigated using the circle criterion for continuous infinite-dimensional systems with unbounded control and observation in the frame of systems in factor form.
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