ABSTRACT
In this chapter, bounded input-bounded output (BIBO) stability of a linear time invariant system will be defined first. Then, BIBO stability of the feedback system formed by a controller C(s) and a plant P(s) can determined by applying the Routh-Hurwitz test on the characteristic polynomial, which is defined from the numerator and denominator polynomials of C(s) and P(s). In engineering applications, the sensor model H(s) is usually a stable transfer function. The Routh-Hurwitz test is a direct procedure for checking stability of a polynomial without computing its roots. The Routh-Hurwitz stability test determines stability of a characteristic polynomial χ(s) with fixed coefficients. If there are only a few uncertain parameters (due to plant uncertainty) or free parameters (of controller) in the coefficients of χ(s), then it is still possible to use the Routh-Hurwitz test to determine the set of all admissible parameters for stability.
