Stabilization of amplitude of oscillations via relay delay control

Time delay does not allow realizing an ideal sliding mode, but implies oscillations in the state space. It is shown that relay delay controllers allow us to achieve stabilization for amplitude of oscillations suppressing uncertainties in a time delay even in the case when the time delay is variable. Sufficient conditions for a relay delay stabilization are found. The obtained results are illustrated in the example of the relay delay stabilization for the inverted pendulum.