A root-locus technique for linear systems with delay

A new method of plotting the root-loci is developed for the linear control system with delay in control or in state. In case of the system with delay in control, the root-locus plot starts from neighborhoods of the open-loop zeros instead of the open-loop poles and thus the effect of time-delay is easily handled. In case of the system with delay in state, the open-loop poles are firstly found by applying the root-locus method for the system with delay in control and then the desired root-loci are found by starting the root-loci plot from the open-loop poles.