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Published March 4, 2015 | Submitted
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A Krein Space Interpretation of the Kalman-Yakubovich-Popov Lemma

Abstract

In this note we give a Krein space interpretation of the celebrated Kalman-Yakubovich-Popov (KYP) Lemma by introducing state-space models driven by inputs that lie in an indefinite-metric space. Such state-space models can be considered as generalizations of standard stochastic statespace models driven by stationary stochastic processes (that lie in a definite, or so-called Hilbert, space). In this framework, the KYP lemma corresponds to a certain decomposition in Krein space.

Additional Information

This work was supported in part by the Air Force Office of Scientific Research, Air Force Systems command under Contract AFOSR91-0060 and by the Army Research Office under contract DAAL03-89-K-0109.

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Created:
August 19, 2023
Modified:
March 5, 2024