Do Unstable Systems Have Amplication and Phase Shift? [Lecture Notes]

Control textbooks sometimes give the impression that amplification and phase shift are properties confined to asymptotically stable systems. For example, [1, p. 400] states that "Any system with a pole in the RHP is unstable; hence it would be impossible to determine its frequency response experimentally because the system would never reach a steady-state sinusoidal response for a sinusoidal input." This statement is correct in reference to an unstable plant operating in open loop but does not consider the case of an unstable plant operating inside a stabilized closed loop.