APPLICATIONS OF THE DUALITY: DETECTABILITY VERSUS STABILIZABILITY IN THE STOCHASTIC FRAMEWORK

Vasile Dragan^†, Ioan-Lucian Popa^‡

Abstract: The aim of this paper is to exploit the property of duality between detectability and stabilizability from the stochastic framework, to derive some results from the domain of control of systems with random parameters. First, we shall derive a dual Barbashin-Krasovski type criterion for asymptotic stability of the zero solution of an Itô differential equation under the conditions when there exists a Lyapunov function with negative semidefinite derivative. Then, we provide a set of necessary and sufficient conditions that guaranty the existence of the bounded on ℝ and stabilizing solution of a forward matrix Riccati differential equation with periodic coefficients arising in concordance with the problem of filtering of a signal generated by a dynamical system modeled by stochastic differential equations of Itô type.

Keywords: stochastic detectability, stochastic stabilizability, Barbashin-Krasovski type criterion, Riccati differential equations of filtering.

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

DOI  10.56082/annalsarscimath.2026.3.77

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^*Accepted for publication on March 14, 2026
^†vasile.dragan@imar.ro, Institute of Mathematics Simion Stoilow of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania and Academy of Romanian Scientists, 3 Ilfov, 050044 Bucharest, Romania
^‡lucian.popa@uab.ro, Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, Gabriel Bethlen 5, Alba Iulia, 510009, Romania and Faculty of Mathematics and Computer Science, Transilvania University of Brasov, luliu Maniu Street 50, Brasov, 500091, Romania

PUBLISHED in

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

Volume 18 no 3, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997