<p>Systems with non-Hermitian Hamiltonians, specially those exhibiting parity-time (PT ) symmetry, are of particular interest as they describe physical open systems with  alanced loss into and gain from the environment. In this context, the study of eigenvalues location and the  corresponding phase transitions as a function of the degree of non-Hermiticity  is analized here using automatic control tools, particularly the Root-Locus technique. This provides insight on the behavior of these systems, allowing to generalize results for higher order ones. The proposed ideas are analyzed in detail for a class of coupled resonant circuit chains.</p>

<p>Systems with non-Hermitian Hamiltonians, specially those exhibiting parity-time (PT ) symmetry, are of particular interest as they describe physical open systems with  alanced loss into and gain from the environment. In this context, the study of eigenvalues location and the  corresponding phase transitions as a function of the degree of non-Hermiticity  is analized here using automatic control tools, particularly the Root-Locus technique. This provides insight on the behavior of these systems, allowing to generalize results for higher order ones. The proposed ideas are analyzed in detail for a class of coupled resonant circuit chains.</p>