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Necessary and Sufficient Conditions for the Existence of the Stabilizing Solutionof the Riccati Equation in a Hilbert Space: A Popov Function Approach

机译：Hilbert空间中Riccati方程稳定解存在的充要条件：popov函数方法

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摘要

A necessary and sufficient condition was given for the existence of thestabilizing solution of a general Riccati equation in an abstract Hilbert space setting where the input operators are assumed to be bounded. This result allowed an extension of a known criterion for J-spectral factorizations. Two particular cases are then considered. Both cases enjoy the property that the solutions to the Riccati equations have an 'optimality' property. The first case is related to the well-known Positivity Theorem and gives the solution to the LQ problem. The second case is shown to give the solution to a max-min quadratic problem. A sufficient condition was given for existence of a positive stabilizing solution of the Riccati equation in this second case. As an application, a central result in H(infinity)-control theory was re-derived.

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