TABLE OF CONTENTS If a transfer function that is a rational function of s has any poles in the right half plane, the transfer function represents an unstable system. We state that this is more generally true-a pole or poles in the right half plane is the sign of an unstable system. No poles in the right half plane is the sign of a stable system.
Much of control theory is devoted to answering the questions "does the transfer function of the system of interest have any poles in the right half plane? Might small changes to the system cause poles to migrate to the right half-plane?" Many of the techniques used to determine the stability of a system assume that the system's transfer function is a rational function of s and that the polynomials in the numerator and the denominator have real coefficients. Any system whose component parts are real gains, integrators and differentiator is of this type. The examples of the previous chapters make it clear that many systems are (at least approximately) of this type.
Some techniques allow other classes of analytic functions as well. All the techniques we consider assume that the transfer function is analytic except for isolated poles. Though this is a strong restriction on the type of system one may use, many practical systems can be described by transfer functions of this type. The most commonly used block whose transfer function is not...
