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

In this article we consider the γ ‐stabilization of n th‐order linear time‐invariant dynamical systems using multiplicity‐induced‐dominancy ‐based controller design in the presence of delays in the input or the output channels. A sufficient condition is given for the dominancy of a real root with multiplicity at least n + 1 and at least n using an integral factorization of the corresponding characteristic function. A necessary condition for γ ‐stabilizability is analyzed utilizing the property that the derivative of a γ ‐stable quasipolynomial is also γ ‐stable under certain conditions. Sufficient and necessary conditions are given for systems with real‐rooted open‐loop characteristic function: the delay intervals are determined where the conditions for dominancy and γ ‐stabilizability are satisfied. The efficiency of the proposed controller design is shown in the case of a multilink inverted pendulum.