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arXiv · 1804.08505

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

J. A. Ball·G. J. Groenewald·S. ter Horst
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Abstract

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

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J. A. Ball, G. J. Groenewald, S. ter Horst. 2018-04-23. Standard versus Bounded Real Lemma with infinite-dimensional state space II: The storage function approach. https://arxiv.org/abs/1804.08505

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