A control design methodology for SISO linear time-delay systems

This paper illustrates a control technique for single-input linear systems with delay in the state. We first proceed by introducing a novel definition of stability called Ω-stability which translate the fact that a system is stable in the Krasovskii sense over a set Ω derived from the negative real side of the complex plane. In other words, all the eigenvalues of the system lies inside the set Ω with a given stability margin. Then, for the control design, the system's model is transformed into an extended Jordan controllable canonical form (JCCF). Based on the JCCF, we proposed a systematic construction of the controller gain such that the system under consideration becomes Ω-stable. The effectiveness of the controller is shown, via simulation, by using a typical academic example.