Structural Interpretations of Stability Tests of Linear Systems

A number of stability-test procedures for continuous-time and discrete-time linear systems have been advanced. Of these, the Routh-Hurwitz stability test for continuous-time systems and Schur-Cohn stability test for discrete-time systems are well-known, and can be found in all texts on linear systems. In this talk, we provide a unified structural interpretation of these two well-known stability tests. The basic idea behind the network interpretation is the fact that the stability of any linear system is equivalent to the stability of a related allpass system. The allpass system can be realized as a cascade of two-pair allpass (lossless) networks. The parent linear system is stable if and only if the allpass two-pair is stable.