Conditions for stabilizability of time?delay systems with real?rooted plant

In this article we consider the -stabilization of nth-order linear time-invariant dynamical systems using multiplicity-induced-dominancy-based controller design in presence delays input or output channels. A sufficient condition is given for dominancy a real root with multiplicity at least and n an integral factorization corresponding characteristic function. necessary -stabilizability analyzed utilizing property that derivative -stable quasipolynomial also under certain conditions. Sufficient conditions are real-rooted open-loop function: delay intervals determined where satisfied. The efficiency proposed shown case multilink inverted pendulum.