ABSTRACT
The advances in two-dimensional (2-D) signal and image processing activities have stimulated active research in 2-D circuits and systems area. Two-variable (2-V) or 2-D Hurwitz polynomial study finds application in areas such as generation and testing of (2-V) reactance functions, bounded/positive real functions, and matrices; testing the stability of 2-D digital filters; and the generation of stable 2-D digital transfer functions. Stability analysis is an important aspect of the design of dynamic systems. This analysis is often carried out by examining for the absence of zeroes of the denominator polynomial of a system transfer function in some specified regions of the complex plane. One dimensional (1-D) systems are studied through the characterization whether or not the denominator polynomial is Hurwitz. By expanding this idea, we can define and study 2-D (also called bivariate, 2-V) Hurwitz polynomials. In view of the diverse needs of several different applications a number of 2-D Hurwitz polynomials have been defined and their test procedures established. In this chapter, a detailed presentation of various 2-D
Hurwitz polynomials and their relationships to one another is given. We also study their relevant applications.
