Nevanlinna test of stability

In this paper, a new test of stability for scalar autonomous systems known as Nevanlinna test of stability is introduced. This test can be derived using the Bézoutian of the characteristic polynomial of a given system. It is shown in this paper that an associated quadratic differential form called the Bézoutian functional is positive if and only if the given system is asymptotically stable. Nevanlinna test of stability proceeds by checking if the Bézoutian functional associated with a given system is positive.