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For discrete-time causal linear input/state/output systems, the Bounded RealLemma explains (under suitable hypotheses) the contractivity of the values ofthe transfer function over the unit disk for such a system in terms of theexistence of a positive-definite solution of a certain Linear Matrix Inequality(the Kalman-Yakubovich-Popov (KYP) inequality). Recent work has extended thisresult to the setting of infinite-dimensional state space and associatednon-rationality of the transfer function, where at least in some casesunbounded solutions of the generalized KYP-inequality are required. This paperis the second installment in a series of papers on the Bounded Real Lemma andthe KYP inequality. We adapt Willems' storage-function approach to theinfinite-dimensional linear setting, and in this way reprove various resultspresented in the first installment, where they were obtained as applications ofinfinite-dimensional State-Space-Similarity theorems, rather than via explicitcomputation of storage functions.

Standard versus Bounded Real Lemma with infinite-dimensional state space II: The storage function approach