Sylvester Equation Controllability

Available identifiers

MaRDI QIDQ6674378

Sylvester equation for the controllability of a linear control system

Description

Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the Lyapunov equations for the calculations of Gramians.

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Defining Formula: $AX+X{\tilde{A}}^{*}+B{\tilde{B}}^{*}=0$

$A$ symbol represents Control System Matrix A

$B$ symbol represents Control System Matrix B

$X$ symbol represents Unknown Matrix

$\tilde{A}$ symbol represents Control System Matrix A (Reduced)

$\tilde{B}$ symbol represents Control System Matrix B (Reduced)

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