SUPER-HIGH-FREQUENCY OSCILLATIONS IN A DISCONTINUOUS DYNAMIC SYSTEM WITH TIME-DELAY

We study oscillations in the discontinuous dynamic system with time delay x(t) = -sign x(t-1) + F(x(t), t), t greater than or equal to 0. This is a typical model of relay feedbacek with delay. It is known that stable modes in this system have a bounded oscillation frequency. Here we consider transient processes and obtain the following result: under some restrictions on F, the average oscillation frequency of any solution becomes finite after a period of time, i.e. super-high-frequency oscillations (with infinite frequency) exist only in a finite time interval. Moreover, we give an effective upper bound on the length of this interval.