Output stabilization of a class of second-order linear time-delay systems: An eigenvalue approach

This paper studies linear time-invariant systems with an input delay and two repeated or distinct real poles. The closed-loop system eigenvalue-loci with respect to the output feedback controller gain are investigated by using the Lambert function and root-locus construction techniques. Output feedback stabilization conditions and stability robustness with respect to the delay time uncertainty are established. Also, the response performance is discussed. Three examples and related simulations are presented to illustrate the analysis results.