Observability Gramian (Generalized) (Q6674005): Difference between revisions

From MaRDI portal

Jump to:navigation, search

Latest revision as of 13:51, 30 July 2025

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

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

Statements

0 references

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}

0 references

in defining formula

A

symbol represents

Control System Matrix A

0 references

C

symbol represents

Control System Matrix C

0 references

N

symbol represents

Control System Matrix N

0 references

t

symbol represents

0 references

W_{o}

symbol represents

Observability Gramian (Generalized)

0 references

0 references

MaRDI profile type

MaRDI quantity profile

0 references

Jørgen Pedersen Gram

0 references

Observability Gramian

0 references

Sitelinks

Mathematics(1 entry)

mardi Quantity:6674005

Retrieved from "https://mardi.schubotz.org/w/index.php?title=Item:Q6674005&oldid=43519272"