CONTROL DESIGN FOR A MULTIDIMENSIONAL SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS WITH RELAY HYSTERESIS AND PERTURBATION

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Abstract

A multidimensional controllable system with a constant matrix, a significant nonlinearity of the twoposition relay type with hysteresis as a control and a continuous periodic perturbation function is considered. The system matrix has simple, real, non-zero eigenvalues, among which one can be positive. Conditions for the system parameters, including the nonlinearity ones, are established under which there is a single two-point oscillatory periodic solution with a period comparable to the period of the perturbation function in the case of a special type of the feedback vector. The asymptotic stability of the solution has been proven using the phase plane method. The results obtained are illustrated by examples for three-dimensional systems.

About the authors

V. V Yevstafyeva

Saint Petersburg State University

Email: v.evstafieva@spbu.ru
Russia

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