Sylvester, Lyapunov, and algebraic Riccati equations are the bread and butter of control theorists . They are used to compute infinite-horizon Gramians, solve optimal control problems in continuous or discrete time, and design observers . Here, we derive the forward and reverse-mode derivatives of the solutions to all three types of equations, and showcase their application on an inverse control problem .

Author(s) : Ta-Chu Kao, Guillaume Hennequin

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Keywords : control - equations - lyapunov - algebraic - riccati -

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