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JOURNALS // Avtomatika i Telemekhanika // Archive

Avtomat. i Telemekh., 2008 Issue 12, Pages 3–40 (Mi at761)

This article is cited in 107 papers

Surveys

$D$-decomposition technique state-of-the-art

E. N. Gryazina, B. T. Polyak, A. A. Tremba

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: It is a survey of recent extensions and new applications for the classical $D$-decomposition technique. We investigate the structure of the parameter space decomposition into root invariant regions for single-input single-output systems linear depending on the parameters. The $D$-decomposition for uncertain polynomials is considered as well as the problem of describing all stabilizing controllers of the certain structure (for instance, PID-controllers) that satisfy given $H_\infty$. It is shown that the $D$-decomposition technique can be naturally linked with $M-\Delta$ framework (a general scheme for analysis of uncertain systems) and it is applicable for describing feasible sets for linear matrix inequalities. The problem of robust synthesis for linear systems can be also treated via $D$-decomposition technique.

PACS: 02.30.Yy

Presented by the member of Editorial Board: A. P. Kurdyukov

Received: 24.12.2007


 English version:
Automation and Remote Control, 2008, 69:12, 1991–2026

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© Steklov Math. Inst. of RAS, 2025