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Controllability Gramian (Generalized) - MaRDI portal

Controllability Gramian (Generalized) (Q6674004)

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

Language	Label	Description	Also known as
English	Controllability Gramian (Generalized)	generalized Gramian of controllability, for use in bi-linear control problems

Statements

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defining formula

\begin{aligned} 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{aligned}

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in defining formula

A

symbol represents

Control System Matrix A

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B

symbol represents

Control System Matrix B

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N

symbol represents

Control System Matrix N

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t

symbol represents

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W_{c}

symbol represents

Controllability Gramian (Generalized)

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MaRDI profile type

MaRDI quantity profile

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Jørgen Pedersen Gram

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Controllability Gramian

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Sitelinks

Mathematics(1 entry)

mardi Quantity:6674004

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