Some insights on rightmost spectral values assignment for time delay systems

This paper investigates the stability and stabilization of some generic linear second-order time-invariant retarded system with single delay. It provides an appropriate stability criterion based on the manifold defined by the coexistence of the maximal number of negative spectral values. Next, such ideas are exploited in the context of delayed output feedback by an appropriate "partial" pole placement guaranteeing simultaneously the stability in closed-loop and an appropriate exponential decay rate. To perform such an analysis, the argument principle is explicitly used.