THE MEAN-SQUARE STABILITY AND MEAN-SQUARE STABILIZABILITY OF THE DISCRETE-TIME MEAN-FIELD STOCHASTIC LINEAR SYSTEMS WITH PERIODIC COEFFICIENTS

Vasile Drăgan†

Abstract: In this work, several aspects of the mean-square stability and of the mean-square stabilizability of a class of discrete-time mean-field stochastic linear systems (MFSLS) with periodic coefficients is addressed. To a discrete-time MFSLS one associates in a natural way a companion standard discrete-time stochastic linear system (DTSLS). Our aim is to compare the mean-field exponential stability in mean-square (MFESMS) property of the MFSLS under consideration with the exponential stability in mean-square (ESMS) property of its companion DTSLS. Even if in some already published works is asserted that the two concepts of exponential stability are equivalent, we show that this equivalence is not true. We also show that the MF mean-square stabilizability of a discrete-time controlled MFSLS is not equivalent to the mean-square stabilizability of its controlled companion DTSLS.

Keywords: mean-field stochastic linear systems, mean-square stability, mean-square stabilizability, periodic coefficients.

MSC: 93E15, 93B05, 93B07, 93D15, 47B65.

DOI 10.56082/annalsarscimath.2026.4.339

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*Accepted for publication on October 19, 2026
†Vasile.Dragan@imar.ro, Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O.Box 1-764, RO-014700, Bucharest, Romania; Academy of Romanian Scientists, Str. Ilfov, 3, Bucharest, Romania

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 4, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997