Stretched exponential function: Difference between revisions

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The '''Kalman–Yakubovich–Popov lemma''' is a result in [[system analysis]] and [[control theory]] which states: Given a number <math>\gamma > 0</math>, two n-vectors b, c and an n by n [[Hurwitz matrix]] A, if the pair <math>(A,b)</math> is completely [[controllability|controllable]], then a symmetric matrix P and a vector q satisfying
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:<math>A^T P + P A = -q q^T\,</math>
 
:<math> P b-c = \sqrt{\gamma}q\,</math>
 
exist if and only if
:<math>
\gamma+2 Re[c^T (j\omega I-A)^{-1}b]\ge 0
</math>
Moreover, the set <math>\{x: x^T P x = 0\}</math> is the unobservable subspace for the pair <math>(A,b)</math>.
 
The lemma can be seen as a generalization of the [[Lyapunov equation]] in stability theory. It establishes a relation between a [[linear matrix inequality]] involving the [[state space]] constructs A, b, c and a condition in the [[frequency domain]].
 
It was derived in 1962 by [[Rudolf Kalman|Kalman]], who brought together results by [[Vladimir Andreevich Yakubovich]] and [[Vasile M. Popov|Vasile Mihai Popov]].
 
{{DEFAULTSORT:Kalman-Yakubovich-Popov Lemma}}
[[Category:Lemmas]]
[[Category:Stability theory]]

Latest revision as of 12:15, 11 December 2014

The name of the writer is Nestor. Kansas is exactly where her house is but she needs to transfer because of her family members. My occupation is a messenger. What she loves performing is taking part in croquet and she is attempting to make it a occupation.

my page ... http://89.1.13.189/index.php?mod=users&action=view&id=63366

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