Criterion for the Existence of Two-Point Oscillatory Solution     of a Perturbed System with a Relay

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.

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Criterion for the Existence of Two-Point Oscillatory Solution of a Perturbed System with a Relay

Cited by 3 publications

References 16 publications

On One Type of Oscillatory Solutions of a Nonautonomous System with Relay Hysteresis

On One Type of Oscillatory Solutions of a Nonautonomous System with Relay Hysteresis

Closed-Form Calculation of the Fixed Point of the Operator Generated by a Multidimensional System with Relay Hysteresis

Control Design for a Multidimensional System of Ordinary Differential Equations With Relay Hysteresis and Perturbation

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