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

Abstract

AbstractIn this article we consider the ‐stabilization of nth‐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 and at least n using an integral factorization of the corresponding characteristic function. A necessary condition for ‐stabilizability is analyzed utilizing the property that the derivative of a ‐stable quasipolynomial is also ‐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 ‐stabilizability are satisfied. The efficiency of the proposed controller design is shown in the case of a multilink inverted pendulum.