Stretched exponential function - Revision history

en>Inwind: /* History and further applications */clean up, disamb using AWB

2014-12-11T10:15:26Z

History and further applications: clean up, disamb using AWB

← Older revision		Revision as of 12:15, 11 December 2014
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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~~		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.<br><br>my page ... [http://89.1.13.189/index.php?mod=users&action=view&id=63366 http://89.1.13.189/index.php?mod=users&action=view&id=63366]
	:~~<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]~~]

174.21.178.252: made "characteristic function" point to "characteristic function (probability theory)" instead of "characteristic state function"

2014-01-24T03:24:58Z

made "characteristic function" point to "characteristic function (probability theory)" instead of "characteristic state function"

← Older revision		Revision as of 05:24, 24 January 2014
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	~~Hello and welcome. My name~~ is ~~Irwin~~ and ~~I totally dig that name. It's not~~ a ~~typical factor but what she likes performing~~ is ~~base jumping~~ and ~~now she is trying to earn cash with it. North Dakota is our birth location. My working day job is~~ a ~~meter reader.~~<br><br>~~Visit my site~~ - [~~http~~://~~www~~.~~videokeren~~.~~com/blog/71062 home std test~~]		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
			:<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]]

84.153.24.147: /* Fourier Transform */ citation to right place

2012-09-01T12:50:25Z

Fourier Transform: citation to right place

New page

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