CDS 110b: Norms of Signals and Systems - Revision history

Murray: /* Lecture Materials */

2006-02-21T19:52:01Z

Lecture Materials

← Older revision		Revision as of 19:52, 21 February 2006
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	== Lecture Materials ==		== Lecture Materials ==
	* ~~{{cds110b-pdfs\|L7-1_sysnorm.mp3\|MP3 of lecture}} (blackboard~~ lecture; no slides)		* Blackboard lecture; no slides. MP3 lost (technical error)
	* {{cds110b-pdfs\|sysnorm.pdf\|Lecture Notes on system norms}}		* {{cds110b-pdfs\|sysnorm.pdf\|Lecture Notes on system norms}}
	* Reading: DFT, Chapter 2		* Reading: DFT, Chapter 2

Murray: /* Lecture Materials */

2006-02-21T19:50:14Z

Lecture Materials

← Older revision		Revision as of 19:50, 21 February 2006
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	== Lecture Materials ==		== Lecture Materials ==
	~~<!--~~ * {{cds110b-pdfs\|L7-1_sysnorm.mp3\|MP3 of lecture}} (blackboard lecture; no slides) ~~-->~~		* {{cds110b-pdfs\|L7-1_sysnorm.mp3\|MP3 of lecture}} (blackboard lecture; no slides)
	* {{cds110b-pdfs\|sysnorm.pdf\|Lecture Notes on system norms}}		* {{cds110b-pdfs\|sysnorm.pdf\|Lecture Notes on system norms}}
	* Reading: DFT, Chapter 2		* Reading: DFT, Chapter 2
	* {{cds110b-pdfs\|hw6.pdf\|HW #6}} (due 22 Feb)		* {{cds110b-pdfs\|hw6.pdf\|HW #6}} (due 22 Feb)

Murray: /* Lecture Materials */

2006-02-14T06:38:37Z

Lecture Materials

← Older revision		Revision as of 06:38, 14 February 2006
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	* {{cds110b-pdfs\|sysnorm.pdf\|Lecture Notes on system norms}}		* {{cds110b-pdfs\|sysnorm.pdf\|Lecture Notes on system norms}}
	* Reading: DFT, Chapter 2		* Reading: DFT, Chapter 2
			* {{cds110b-pdfs\|hw6.pdf\|HW #6}} (due 22 Feb)

	== References and Further Reading ==		== References and Further Reading ==

Murray: /* Frequently Asked Questions */

2006-02-14T04:49:48Z

Frequently Asked Questions

← Older revision		Revision as of 04:49, 14 February 2006
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	'''Q: So you ''can'' do pole zero cancellations?'''		'''Q: So you ''can'' do pole zero cancellations?'''
	<blockquote>		<blockquote>
	As long as they don't occur in the closed right half plane, pole zero cancellations are OK from the point of view of stability. It is generally not a good idea to rely on exact cancellations even if they are stable cancellations (LHP), but they are relatively benign.		<p>As long as they don't occur in the closed right half plane, pole zero cancellations are OK from the point of view of stability. It is generally not a good idea to rely on exact cancellations even if they are stable cancellations (LHP), but they are relatively benign. </p>

	Exercise: try plotting the frequency response for		<p>Exercise: try plotting the frequency response for
	<center><math>		<center><math>
	P(s) = \frac{s - 1}{s - 1 + \epsilon}		P(s) = \frac{s - 1}{s - 1 + \epsilon}
	</math></center>		</math></center>
			</p>
			</blockquote>

			'''Q: I'm not sure if I really understand what "sup" is'''
			<blockquote>
			Formally, the supremum (sup) of a set is the smallest real number that is larger than or equal to every element in the set. For a real-valued function <math>f(x)</math>, <math>\sup_x f(x)</math> is smallest real number <math>y</math> such that <math>f(x) \leq y</math>. Here's a pretty good [http://en.wikipedia.org/wiki/Supremum Wikipedia article on supremum].
	</blockquote>		</blockquote>

Murray: /* Frequently Asked Questions */

2006-02-14T04:44:34Z

Frequently Asked Questions

← Older revision		Revision as of 04:44, 14 February 2006
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	== Frequently Asked Questions ==		== Frequently Asked Questions ==
			'''Q: So you ''can'' do pole zero cancellations?'''
			<blockquote>
			As long as they don't occur in the closed right half plane, pole zero cancellations are OK from the point of view of stability. It is generally not a good idea to rely on exact cancellations even if they are stable cancellations (LHP), but they are relatively benign.

			Exercise: try plotting the frequency response for
			<center><math>
			P(s) = \frac{s - 1}{s - 1 + \epsilon}
			</math></center>
			</blockquote>

Murray: CDS 110b:Norms of Signals and Systems moved to CDS 110b: Norms of Signals and Systems

2006-02-14T04:39:35Z

CDS 110b:Norms of Signals and Systems moved to CDS 110b: Norms of Signals and Systems

← Older revision		Revision as of 04:39, 14 February 2006
(No difference)

Murray: /* Lecture Materials */

2006-02-14T04:36:33Z

Lecture Materials

← Older revision		Revision as of 04:36, 14 February 2006
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	== Lecture Materials ==		== Lecture Materials ==
	* {{cds110b-pdfs\|L7-1_sysnorm.mp3\|MP3 of lecture}} (blackboard lecture; no slides)		<!-- * {{cds110b-pdfs\|L7-1_sysnorm.mp3\|MP3 of lecture}} (blackboard lecture; no slides) -->
	* {{cds110b-pdfs\|sysnorm.pdf\|Lecture Notes on system norms}}		* {{cds110b-pdfs\|sysnorm.pdf\|Lecture Notes on system norms}}
	* Reading: DFT, Chapter 2		* Reading: DFT, Chapter 2

Murray at 04:36, 14 February 2006

2006-02-14T04:36:17Z

New page

{{cds110b-wi06}}
This lecture provides an introduction to some of the signals and systems concepts required for the study of robust (<math>H_\infty</math>) control. __NOTOC__

== Lecture Outline ==
<ol type=I>
<li> Norms of linear systems (con't)
<li> Internal stability
</ol>

== Lecture Materials ==
* {{cds110b-pdfs|L7-1_sysnorm.mp3|MP3 of lecture}} (blackboard lecture; no slides)
* {{cds110b-pdfs|sysnorm.pdf|Lecture Notes on system norms}}
* Reading: DFT, Chapter 2

== References and Further Reading ==

== Frequently Asked Questions ==