Adaptive Simpson's method: Difference between revisions

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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]].
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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}}

Latest revision as of 08:22, 24 May 2014

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