Matrix norm approach for control of linear time-delay systems

The aim of this paper is to present some results on the control synthesis of time-delay linear systems. Our objective is to find linear controllers able to increase the first stability window imposing that the delay-free system is stable. Our method treats time-delay systems control design with numeric routines based on Linear Matrix Inequalities (LMI) arisen from classical linear time invariant system theory coupled together with a unidimensional search. The proposed algorithm is simple, efficient and easy to be numerically implemented. Some examples illustrating state and output feedback design are solved and discussed in order to shed the light on the most relevant characteristic of the theoretical results. The paper ends with some discussion on further theoretical extensions of the proposed methodology.