On controllers performance for a class of time-delay systems: Maximum decay rate

This paper states some results aiming at finding the parameters of a controller that provides the maximum decay rate of the closed-loop response for a linear time-invariant time-delay system. These results help to understand the behavior of dominant roots and the spectral abscissa under parametric variations, including the delay. The controller parameters or points of best performance are obtained for compact subsets of the system's stability region. In addition, it is shown that these points are not always related to obtaining a multiple dominant root or the existence of a root of maximal multiplicity. To illustrate the effectiveness and diversity of application of the proposed results, four key examples from the literature were chosen and the points of best performance were found. (c) 2022 Elsevier Ltd. All rights reserved.