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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.
2000 Mathematics Subject Classification::
Acknowledgement
The author thanks anonymous referee whose suggestions helped to improve the exposition of the results.
Notes
1. It is enough to assume that N is hemicontinuous, however we shall not need such a level of generality.
2. A short separate proof shows that actually H>0 thanks to PS of and the observability of
,
, equivalent to the observability of
as
.