Slyn'ko, V., ITunc, CemilBivziuk, V. O.2025-05-102025-05-1020210265-07541471-688710.1093/imamci/dnaa0032-s2.0-85114194565https://doi.org/10.1093/imamci/dnaa003https://hdl.handle.net/20.500.14720/7192Vitaliy, Slyn'Ko/0000-0002-2321-922XThe paper deals with the problem of stabilizing the equilibrium states of a family of non-linear non-autonomous systems. It is assumed that the nominal system is a linear controlled system with periodic coefficients. For the nominal controlled system, a new method for constructing a Lyapunov function in the quadratic form with a variable matrix is proposed. This matrix is defined as an approximate solution of the Lyapunov matrix differential equation in the form of a piecewise exponential function based on partial sums of a W. Magnus series. A stabilizing control in the form of a linear feedback with a piecewise constant periodic matrix is constructed. This control simultaneously stabilizes the considered family of systems. The estimates of the domain of attraction of an asymptotically stable equilibrium state of a closed-loop system that are common for all systems are obtained. A numerical example is given.eninfo:eu-repo/semantics/closedAccessCommutator CalculusLyapunov'S Direct MethodNon-Linear Control SystemsRobust ControlStabilityUncertain SystemsArticle381Q2Q2125142WOS:000651813900007