Final answer:
The issue asks to find the range of K that ensures the stability of a given control system by applying stability criteria and confirming that the system's poles lie in the left half of the complex plane.
Step-by-step explanation:
The question involves finding the range of K for stability of a unity-feedback control system with a given open-loop transfer function. To address this, one would need to apply control system stability criteria, such as the Routh-Hurwitz criterion, to determine the values of K that would result in a stable system. Specifically, this requires analysis of the system's characteristic equation and checking the number of poles in the left half of the complex plane. The task involves finding the values of K for which all the roots of the characteristic equation have negative real parts, indicating a stable system.