Observability Gramian (Generalized)

Available identifiers

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

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

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