A techebycheff approximation approach to the computation of stabilizing compensators for systems with delays

It is shown that the problem of computing, the stabilizing compensators for a class of delay-differential systems, including neutral ones as in [1], can be approached using certain results on Tchebycheff approximation [3] and some related optimization techniques [4,5]. It is a direct consequence of the results and the single complex variable approach established in [1] for the first time for this problem that one can first compute delay-free (finite dimensional) stabilizing compensators for the systems considered in [1] which also includes a large class of neutral delay-differential systems. Once one stabilizing compensator is computed, the others can be obtained using the results in [2] and in the references there. Here we also show that a well known algorithm of de La Val??e Poussin for the case of real numbers can be extended to the complex case. Also, some literature is discussed (see Remark).