In this article we consider the gamma-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 n+1 and at least
n using an integral factorization of the corresponding characteristic function. A
necessary condition for gamma-stabilizability is analyzed utilizing the property that
the derivative of a gamma-stable quasipolynomial is also gamma-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 gamma-stabilizability are satisfied. The efficiency of the proposed
controller design is shown in the case of a multilink inverted pendulum.
