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$$D$$-decomposition technique state-of-the-art. (English. Russian original) Zbl 1160.93003
Autom. Remote Control 69, No. 12, 1991-2026 (2008); translation from Avtom. Telemekh. 2008, No. 12, 3-40 (2008).
Summary: 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 $$H _{\infty }$$-criterion. 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.

##### MSC:
 93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory 93B40 Computational methods in systems theory (MSC2010) 93C05 Linear systems in control theory 65F05 Direct numerical methods for linear systems and matrix inversion 93B50 Synthesis problems
YALMIP
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