Semiglobal stabilization via relay controller with uncertain time delay

Sufficient conditions for relay delayed semiglobal stabilization of linear systems are found connecting the upper bound of uncertainty in a time delay and the maximum of the real part of system spectrum. Algorithm of delayed relay control gain adaptation for semiglobal stabilization is suggested using delayed information about amplitude of oscillations. Proposed algorithm rejects bounded uncertainties in the time delay: once being designed for the upper bound of uncertainty in the time delay for given system this relay delayed control law ensure semiglobal stabilization for any values of the time delay less than the upper bound even in the case when the delay is variable.