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Stabilization of linear control systems and pole assignment problem: a survey. (English. Russian original) Zbl 1453.93098

Vestn. St. Petersbg. Univ., Math. 52, No. 4, 349-367 (2019); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 6(64), No. 4, 564-591 (2019).
Summary: This paper reviews the problems of stabilization and pole assignment in the control of linear time-invariant systems using the static state and output feedback. The main results are presented, along with a literature review. Stationary and nonstationary stabilizations with the static feedback are considered. The algorithms of low- and high-frequency stabilization of linear systems for solving Brockett’s stabilization problem are provided. The effective necessary and sufficient conditions for stabilization of two- and three-dimensional controllable linear systems are given in terms of the system parameters. The pole assignment problem and the related issues for linear systems are considered.

MSC:

93B55 Pole and zero placement problems
93D20 Asymptotic stability in control theory
93B52 Feedback control
93C05 Linear systems in control theory
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
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