en>Rjwilmsi: Added 2 dois to journal cites using AWB (10209)

2014-05-24T07:22:44Z

Added 2 dois to journal cites using AWB (10209)

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	~~The~~ ''~~'Observability Gramian''' is~~ a ~~[[Gramian]] used~~ in ~~[[optimal control]] theory to determine whether or not a linear system is [[Observability\|observable]].~~		Jayson Berryhill is how I'm known as and my spouse doesn't like it at all. I am presently a travel agent. My wife and I live in Mississippi and I love psychic ([http://mybrandcp.com/xe/board_XmDx25/107997 mybrandcp.com]) each day living here. The favorite hobby for him and his children is to play lacross and he would never give it up.

	~~For a linear system described by~~

	~~<math>\dot{x} = A x + B u</math>~~

	~~<math>y = C x + D u \,</math>~~

	~~The observability Gramian for a linear time invariant system is given by~~

	~~<math>W_o (t) = \int\limits_0^t e^{A^T \tau} C^T C e^{A \tau} d\tau</math>~~

	If and ~~only if the matrix <math>W_o</math> is [[nonsingular]] for every <math>t > 0</math>, the pair <math>~~(~~A,C)</math> is observable.~~

	~~==See also==~~
	*[[Controllability Gramian]]
	*[[Gramian matrix]]

	~~==References==~~
	~~{{unreferenced\|date=July 2008}}~~

	~~==External links==~~
	*[http://~~reference.wolfram~~.com/~~mathematica~~/~~ref~~/~~ObservabilityGramian~~.~~html Mathematica function~~ to ~~compute the observability Gramian]~~

	~~[[Category:Control theory]]~~


	~~{{applied-math-stub}}~~

217.22.0.226 at 12:21, 6 August 2012

2012-08-06T12:21:13Z

New page

The '''Observability Gramian''' is a [[Gramian]] used in [[optimal control]] theory to determine whether or not a linear system is [[Observability|observable]].

For a linear system described by

<math>\dot{x} = A x + B u</math>

<math>y = C x + D u \,</math>

The observability Gramian for a linear time invariant system is given by

<math>W_o (t) = \int\limits_0^t e^{A^T \tau} C^T C e^{A \tau} d\tau</math>

If and only if the matrix <math>W_o</math> is [[nonsingular]] for every <math>t > 0</math>, the pair <math>(A,C)</math> is observable.

==See also==
*[[Controllability Gramian]]
*[[Gramian matrix]]

==References==
{{unreferenced|date=July 2008}}

==External links==
*[http://reference.wolfram.com/mathematica/ref/ObservabilityGramian.html Mathematica function to compute the observability Gramian]

[[Category:Control theory]]

{{applied-math-stub}}

Adaptive Simpson's method - Revision history

en>Rjwilmsi: Added 2 dois to journal cites using AWB (10209)

217.22.0.226 at 12:21, 6 August 2012