Controllability Gramian (Generalized)

Available identifiers

generalized Gramian of controllability, for use in bi-linear control problems

Defining Formula: $\begin{matrix} W_{c} & \equiv & \sum_{j = 1}^{\infty} \int_{0}^{\infty} \dots \int_{0}^{\infty} P_{j} (t_{1}, \dots t_{j}) P_{j}^{*} (t_{1}, \dots t_{j}) d t_{1} \dots d t_{j} \\ P_{1} (t_{1}) & \equiv & e^{A t_{1}} i B \\ P_{j} (t_{1}, \dots, t_{j}) & \equiv & e^{A t_{j}} i N P_{j - 1} \end{matrix}$
$A$ symbol represents Control System Matrix A
$B$ symbol represents Control System Matrix B
$N$ symbol represents Control System Matrix N
$t$ symbol represents Time
$W_{c}$ symbol represents Controllability Gramian (Generalized)

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