Stability Analysis: Linear Approaches

This chapter illustrates the use of the Routh-Hurwitz test, and the application of the Nyquist stability criterion. Employing Routh-Hurwitz and Nyquist stability analyses, show that administration of inhaled 02 would eliminate Cheyne-Stokes breathing in the patient with congestive heart failure. The chapter employs a more intuitive approach by illustrating the basic notions underlying the Nyquist stability criterion. It considers the linear lung mechanics model with proportional feedback. As in the example of the lung mechanics model, the transient response and stability of the systems are determined by the poles of their closed-loop transfer functions. The relative stability of a given system can be quantified in terms of either the gain margin or the phase margin. The chapter also illustrates how the root locus method is applied. It concludes from Routh-Hurwitz analysis that the normal pupillary reflex is a highly stable negative feedback system.