O.V. Druzhinina - Dr.Sc. (Phys.-Math.), Professor, Dorodnicyn Computing Center of RAS E-mail: ov-druzh@mail.ru O.N. Masina - Dr.Sc. (Phys.-Math.), Assistant Professor, Department of Automated Systems of Control and Mathematical softwAre, Yelets State University named after I.A. Bunin, E-mail: olga121@inbox.ru

Stability conditions and stabilization of systems with discontinuous right parts are considered. For receiving conditions are used locally Lipschitz-continuous and regular Lyapunov-s functions. Stability for a case of differential inclusions is investigated. Approach to studying of stability of nonlinear systems on the basis of the principle of reduction of problem of stability of solutions of differential inclusions to problem of stability of solutions of fuzzy differential equations is developed. The principle of reduction and stability conditions allow to investigate stability of controlled systems described by differential inclusions and the indistinct differential equations, containing control function in the right parts. In this case the principle of reduction assumes transition from differential inclusion to the corresponding fuzzy differential equation taking into account the additional conditions imposed on control. The considered stability conditions and stabilization can find application in problems of development and improvement of controlled technical systems.

 

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