An Approach to the Stabilization Problem of a Parametrically Uncertain Linear Nonstationary System

Corresponding Member of RAS A. V. Ilin^a^,^b^,^c^,*, P. A. Krylov^b^,**, and A. S. Fursov^a^,^b^,^d^,^e^,***

^aDepartment of Mathematics, School of Science Hangzhou, Dianzi University, Hangzhou, P.R. China

^bFaculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, 119992 Russia

^cFederal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333 Russia

^dBauman Moscow State Technical University (National Research University), Moscow, 105005 Russia

^eInstitute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, 127051 Russia

Correspondence to: *e-mail: iline@cs.msu.su
Correspondence to: **e-mail: pavel@leftsystem.ru
Correspondence to: ***e-mail: fursov@cs.msu.ru

Received 8 July, 2020

Abstract—An approach based on the method of predictive models and the method of superstabilization is proposed to solve the problem of stabilization of parametrically uncertain linear nonstationary systems. The parametric uncertainty is specified using a family of compact sets in the space of square matrices. This approach is rigorously justified for second-order systems, but can be generalized to systems of arbitrary order.

Keywords: stabilization theory, stabilization of linear nonstationary systems, controllability

DOI: 10.1134/S1064562420050452