| Abstract: | We analyse the stability properties of the linear retarded differential-difference equation (RDDE) that arises in the study of adaptive control of pure delay systems. Three different results are given. Firstly, using Floquet theory necessary and sufficient conditions for stability are established for the case of periodic signals of specified frequencies. Secondly, the theory of averaging is used to derive stability-instability conditions under slow adaptation. Finally, a globally stable modified adaptive regulator for systems with known, possibly time-varying, time delay is presented. Two alternative proofs of the latter results are given. One based on the method of Lyapunov functionals and the second one using a Razumikhin-type theorem. |
