Stability of Systems with Multiple Time Delays

Systems whose dynamical representations involve multiple transportation lags are generally difficult to analyse. Such systems give rise to infinite strings of poles in the complex plane and subsequently, transfer functions of a transcendental nature. A Nyquist stability analysis of a system with two delay terms reveals a central region of stability even though the system has an infinite number of poles with positive real parts. An input-output stability criterion due to Zadeh is used to confirm the Nyquist analysis and show that systems with an infinite number of poles are not necessarily subject to the same pole location restrictions as systems with a finite number of poles.