ABSTRACT
Systems have several properties—such as controllability, observability, stability, and invertibility—that play a very decisive role in their behavior. The stability of linear, time-invariant systems is studied in connection with each of the three well-established mathematical models of a system—namely, the state equations, the transfer function matrix, and the impulse response matrix. The most popular algebraic criteria are the Routh, Hurwitz, and the continued fraction expansion criteria. The main characteristic of these three algebraic criteria is that they determine whether or not a system is stable by using a very simple numerical procedure, which circumvents the need for determining the roots of the characteristic polynomial. The Hurwitz criterion determines whether or not the characteristic polynomial has roots in the right-half complex plane.
