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It is shown that an LTI system is a relaxation system if and only if itsHankel operator is cyclic monotone. Cyclic monotonicity of the Hankel operatorimplies the existence of a storage function whose gradient is the Hankeloperator. This storage is a function of past inputs alone, is independent ofthe state space realization, and admits a generalization to nonlinear circuitelements.

Relaxation systems and cyclic monotonicity