A direct frequency domain approach to stability of linear systems with time-varying delays

The stability of linear systems with uncertain time-varying delays from given segments is analyzed. Under assumption that the system is stable for some known constant values of the delays, a sufficient stability condition is derived in terms of the system matrices and the lengths of the delay segments. Different from the existing frequency domain methods which usually apply the small gain theorem, the suggested approach is based on the direct application of the Laplace transform to the transformed system and on the bounding technique in L₂. Numerical examples illustrate the efficiency of the method