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1980•IEEE Transactions on Automatic ControlRequires access

A necessary and sufficient condition for the solution of the Riccati equation to be periodic

T. Sasagawa

Open publisher page 12 citations

Abstract

Assuming that the solution of the autonomous Riccati differential equation exists for allt \geq 0, we give a necessary and sufficient condition for the solution to be periodic. At the same time, from this condition one can readily obtain the period of this periodic solution. Similar results are shown for the discrete and nonautonomous Riccati equations.

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What this paper is about

Assuming that the solution of the autonomous Riccati differential equation exists for allt \geq 0, we give a necessary and sufficient condition for the solution to be periodic. At the same time, from this condition one can readily obtain the period of this periodic solution. Similar results are shown for the discrete and nonautonomous Riccati equations.

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Assuming that the solution of the autonomous Riccati differential equation exists for allt \geq 0, we give a necessary and sufficient condition for the solution to be periodic. At the same time, from this condition one can readily obtain the period of this periodic solution. Similar results are shown for the discrete and nonautonomous Riccati equations.

Key concepts: Riccati equation, Algebraic Riccati equation, Mathematics, Differential equation, Linear-quadratic regulator, Applied mathematics, Period (music), Differential (mechanical device)

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