Elsevier

Automatica

Volume 27, Issue 4, July 1991, Pages 711-715
Automatica

Brief paper
Robust characteristic polynomial assignment

https://doi.org/10.1016/0005-1098(91)90062-7Get rights and content

Abstract

In this paper a computational method for designing controllers which attempt to place the characteristic polynomial of an uncertain system inside some prescribed region is presented. An objective function consisting of two terms is proposed, penalizing both the distance to a given controller and the size of the uncertainty region developed to solve the robust assignment problem. The algorithm is based on semi-infinite programming theory, and the special structure of the problem is exploited to get both simpler methods and convergence proof. The way in which the uncertain parameters affect the plant coefficients is realistic, since it includes multinomial dependence. An example of application is given to illustrate the approach.

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    The main hindrance of the parametric methods is the well-known fact that the stability domain in the space of polynomial coefficients is non-convex in general. That is why several convex approximations of the stability region such as ellipsoids (Galafiore & El Ghaoui, 2004; Henrion, Peaucelle, Arzelier, & Šebek, 2003), hyperrectangles (Chapellat & Bhattacharyya, 1989; Katbab & Jury, 1990; Kharitonov, 1978) and polytopes (Ackermann & Kaesbauer, 2003; Jetto, 1999; Nurges & Luus, 2002; Rotstein et al., 1991) are well known and widely used in robust control. In this paper a novel procedure for robust output controller design for discrete-time systems is proposed by the use of a polytopic approach.

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    1996, IEEE Transactions on Automatic Control
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The original version of this paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor R. F. Curtain under the direction of Editor H. Kwakernaak.

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