\(D\)-decomposition technique state-of-the-art. (English. Russian original) Zbl 1160.93003

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

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

Keywords:

\(D\)-decomposition technique; stabilizing controllers; robust synthesis; linear systems

Software:

YALMIP

References:

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