CDS 212, Homework 6, Fall 2010 - Revision history

Sojoudi: /* Reading */

2010-11-07T18:47:46Z

Reading

← Older revision		Revision as of 18:47, 7 November 2010
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	=== Reading ===		=== Reading ===
	[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4X-3VTSW0Y-2&_user=10&_coverDate=06%2F03%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c~~&_searchStrId=1528893102&_rerunOrigin=scholar.google~~&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=~~77673afc1097c2809dd28b860844f55e~~&searchtype=a KYP paper:] (On the Kalman—Yakubovich—Popov lemma, Anders Rantzer)		[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4X-3VTSW0Y-2&_user=10&_coverDate=06%2F03%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=7cadd4d3ff3995a6e887e15c1a57b578&searchtype=a KYP paper:] (On the Kalman—Yakubovich—Popov lemma, Anders Rantzer, 1996)

	=== Problems ===		=== Problems ===

Sojoudi: /* Reading */

2010-11-05T20:21:01Z

Reading

← Older revision		Revision as of 20:21, 5 November 2010
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	=== Reading ===		=== Reading ===
	[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4X-3VTSW0Y-2&_user=10&_coverDate=06%2F03%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1528893102&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=77673afc1097c2809dd28b860844f55e&searchtype=a KYP paper] (On the Kalman—Yakubovich—Popov lemma, Anders Rantzer)		[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4X-3VTSW0Y-2&_user=10&_coverDate=06%2F03%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1528893102&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=77673afc1097c2809dd28b860844f55e&searchtype=a KYP paper:] (On the Kalman—Yakubovich—Popov lemma, Anders Rantzer)

	=== Problems ===		=== Problems ===

Sojoudi: /* Reading */

2010-11-05T20:20:40Z

Reading

← Older revision		Revision as of 20:20, 5 November 2010
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	=== Reading ===		=== Reading ===
	[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4X-3VTSW0Y-2&_user=10&_coverDate=06%2F03%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1528893102&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=77673afc1097c2809dd28b860844f55e&searchtype=a KYP paper]		[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4X-3VTSW0Y-2&_user=10&_coverDate=06%2F03%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1528893102&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=77673afc1097c2809dd28b860844f55e&searchtype=a KYP paper] (On the Kalman—Yakubovich—Popov lemma, Anders Rantzer)

	=== Problems ===		=== Problems ===

Sojoudi: /* Reading */

2010-11-05T17:39:53Z

Reading

← Older revision		Revision as of 17:39, 5 November 2010
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	=== Reading ===		=== Reading ===
	[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4X-3VTSW0Y-2&_user=10&_coverDate=06%2F03%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=~~1524979904~~&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=~~8c10ce1dc59d5d8995645582d27731ca~~&searchtype=a KYP paper]		[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4X-3VTSW0Y-2&_user=10&_coverDate=06%2F03%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1528893102&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=77673afc1097c2809dd28b860844f55e&searchtype=a KYP paper]

	=== Problems ===		=== Problems ===

Sojoudi: /* Problems */

2010-11-03T07:52:40Z

Problems

← Older revision		Revision as of 07:52, 3 November 2010
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	</ol>		</ol>
	</li>		</li>
	<li> Write up a complete proof for the KYP Lemma (you need to reproduce the proof given in the class with all details to make sure you have got the main ideas). For this problem, students can work in small groups (up to 3 students)~~, and that~~ each team needs to hand in only a single write-up.		<li> Write up a complete proof for the KYP Lemma (you need to reproduce the proof given in the class with all details to make sure you have got the main ideas). For this problem, students can work in small groups (up to 3 students); each team needs to hand in only a single write-up.
	</li>		</li>
	</li>		</li>

Sojoudi: Created page with '{{CDS homework | instructor = J. Doyle | course = CDS 212 | semester = Fall 2010 | title = Problem Set #5 | issued = 2 Nov 2010 | due = 11 Nov 2010 }} === Reading === [htt…'

2010-11-03T07:49:41Z

Created page with '{{CDS homework | instructor = J. Doyle | course = CDS 212 | semester = Fall 2010 | title = Problem Set #5 | issued = 2 Nov 2010 | due = 11 Nov 2010 }} === Reading === [htt…'

New page

{{CDS homework
| instructor = J. Doyle
| course = CDS 212
| semester = Fall 2010
| title = Problem Set #5
| issued = 2 Nov 2010
| due = 11 Nov 2010
}}

=== Reading ===
[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4X-3VTSW0Y-2&_user=10&_coverDate=06%2F03%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1524979904&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=8c10ce1dc59d5d8995645582d27731ca&searchtype=a KYP paper]

=== Problems ===
<ol>
<li>
Proof of Lemma 5 in the KYP paper:
<ol type="a">
<li> Use part (i) of Lemma 3 to prove part (iii) of this lemma in the KYP paper. Note that you do not need to prove part (i).</li>
<li> Use part (iii) of Lemma 3 in the KYP paper to prove Lemma 5.</li>
</ol>
(Note: a short proof is given in the paper for both parts (a) and (b); but you must provide a detailed proof for full credit.)
</li>

<li>
Consider the following state space equation:
<center><amsmath>
\dot{x}=ax+bu, \quad y=cx
</amsmath></center>
where a,b,c are some scalers and <amsmath>a<0</amsmath>. Find a necessary and sufficient condition in terms of a, b and c such that <amsmath>||H||_\infty<1</amsmath>, using two different methods:
<ol type="a">
<li>Frequency analysis.</li>
<li>KYP Lemma.</li>
</ol>
</li>
<li> Write up a complete proof for the KYP Lemma (you need to reproduce the proof given in the class with all details to make sure you have got the main ideas). For this problem, students can work in small groups (up to 3 students), and that each team needs to hand in only a single write-up.
</li>
</li>