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Extreme point results for robustness of control systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Extreme point results for robustness of control systems./
Author:	Kang, Hwan Il.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 1992,
Description:	135 p.
Notes:	Source: Dissertations Abstracts International, Volume: 55-01, Section: B.
Contained By:	Dissertations Abstracts International55-01B.
Subject:	Electrical engineering. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9306457
ISBN:	9798208520956

Extreme point results for robustness of control systems.
Kang, Hwan Il.

Extreme point results for robustness of control systems. - Ann Arbor : ProQuest Dissertations & Theses, 1992 - 135 p.

Source: Dissertations Abstracts International, Volume: 55-01, Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 1992.

This item must not be sold to any third party vendors.

This dissertation deals with extreme point results for robustness of control systems. Motivated by robust stabilization of interval plants, this focal point is a fundamental problem involving a family of polynomials obtained via convex combination of "extreme members." The objective is to provide conditions under which stability of the extremes implies stability of the entire family. Although the existing literature contains rather strong extreme point results involving frequency domain analysis, there is a paucity of more direct coefficient space criteria--this dissertation deals mainly with the coefficient space problem. To this end, we introduce a so-called Alternating Hurwitz Minor Condition (AHMC) and show how it can be used to enlarge the class of polynomial families for which extreme point results can be obtained. Related to the AHMC is the so-called Mirror Interlaced Root Condition (MIRC). The MIRC involves the locations of roots rather than coefficients. It turns out that the set of polynomials satisfying the AHMC theory is a superset of the set of polynomials satisfying the MIRC theory. This dissertation also includes ramifications of the AHMC and MIRC theories on robust stability of interval plants with feedback compensation. In contrast to existing literature for first order compensators, the AHMC and the MIRC make it possible to deal with classes of higher order compensators in an extreme point context. The final part of the work involves four counterexamples to some conjectures which one is tempted to make. The first counterexample involves robust stability of a weighted diamond polynomial family with real coefficients. For such families, it is shown that stability of all the extreme polynomials does not guarantee robust stability of the entire family. Second, we show by a counterexample that for a diamond family of complex coefficient polynomials having separate bounds for real and imaginary parts, stability of all the extreme polynomials once again does not guarantee robust stability of the whole family. The third counterexample is related to the robust Schur stability problem for an interval polynomial and the fourth counterexample involves polynomial families which arise when working with unmodelled dynamics.

ISBN: 9798208520956Subjects--Topical Terms:

649834
Electrical engineering.
Subjects--Index Terms:

robust stability

Extreme point results for robustness of control systems.
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100 1 $a Kang, Hwan Il. $3 3686205
245 1 0 $a Extreme point results for robustness of control systems.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 1992
300 $a 135 p.
500 $a Source: Dissertations Abstracts International, Volume: 55-01, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Barmish, B. Ross.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Madison, 1992.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a This dissertation deals with extreme point results for robustness of control systems. Motivated by robust stabilization of interval plants, this focal point is a fundamental problem involving a family of polynomials obtained via convex combination of "extreme members." The objective is to provide conditions under which stability of the extremes implies stability of the entire family. Although the existing literature contains rather strong extreme point results involving frequency domain analysis, there is a paucity of more direct coefficient space criteria--this dissertation deals mainly with the coefficient space problem. To this end, we introduce a so-called Alternating Hurwitz Minor Condition (AHMC) and show how it can be used to enlarge the class of polynomial families for which extreme point results can be obtained. Related to the AHMC is the so-called Mirror Interlaced Root Condition (MIRC). The MIRC involves the locations of roots rather than coefficients. It turns out that the set of polynomials satisfying the AHMC theory is a superset of the set of polynomials satisfying the MIRC theory. This dissertation also includes ramifications of the AHMC and MIRC theories on robust stability of interval plants with feedback compensation. In contrast to existing literature for first order compensators, the AHMC and the MIRC make it possible to deal with classes of higher order compensators in an extreme point context. The final part of the work involves four counterexamples to some conjectures which one is tempted to make. The first counterexample involves robust stability of a weighted diamond polynomial family with real coefficients. For such families, it is shown that stability of all the extreme polynomials does not guarantee robust stability of the entire family. Second, we show by a counterexample that for a diamond family of complex coefficient polynomials having separate bounds for real and imaginary parts, stability of all the extreme polynomials once again does not guarantee robust stability of the whole family. The third counterexample is related to the robust Schur stability problem for an interval polynomial and the fourth counterexample involves polynomial families which arise when working with unmodelled dynamics.
590 $a School code: 0262.
650 4 $a Electrical engineering. $3 649834
650 4 $a Systems design. $3 3433840
653 $a robust stability
690 $a 0544
690 $a 0790
710 2 $a The University of Wisconsin - Madison. $3 626640
773 0 $t Dissertations Abstracts International $g 55-01B.
790 $a 0262
791 $a Ph.D.
792 $a 1992
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9306457