Necessary conditions of Hurwitz polynomials (Q1864956)

This paper gives a new necessary condition for the stability of continuous-time polynomials, or Hurwitz stability. It is a generalization of a result by \textit{A. Borobia} and \textit{S. Dormido} [ibid. 338, 67-76 (2001; Zbl 1018.12003)]. The condition is expressed as a simple set of bilinear inequalities satisfied by the polynomial coefficients. The proof, technical but quite original and interesting, relies on the Hermite-Bieler theorem and the Lagrange multiplier method for nonlinear optimization. The result may have applications in systems control theory, where these conditions can be used for stability analysis or design. Interestingly, the paper refers to another bilinear stability condition presented at a Chinese meeting in 1957. Similar conditions, not referenced in the paper and derived independently via a totally different approach, can be found in [\textit{A. V. Lipatov} and \textit{N. I. Sokolov}, Autom. Remote Control 39, 1285-1291 (1979; Zbl 0427.93040)].