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Abstract: The structure of positive polynomials on a torus is derived from recent results of real algebraic geometry. As an application, we propose some simple conditions for testing the hyperbolicity/stability of a generic class of linear systems of retarded type. [Copyright &y& Elsevier]

In this paper, which is a direct continuation and generalization of the recent works by the authors [17, 35], we show the validity of the generic multiplicity-induced-dominancy property for a general class of linear functional differential equations with a single delay, including the retarded as well as the neutral cases. The result is based on an appropriate integral representation of the corresponding characteristic quasipolynomial functions involving some appropriate degenerate hypergeometric functions. [ABSTRACT FROM AUTHOR]

This work exploits structural properties of a class of functional Vandermonde matrices to emphasize some qualitative properties of a class of linear autonomous nth order differential equation with forcing term consisting in the delayed dependent-variable. More precisely, it deals with the stabilizing effect of delay parameter coupled with the coexistence of the maximal number of real spectral values. The derived conditions are necessary and sufficient and, to the best of the authors’ knowledge, represent a novelty in the literature. Under appropriate conditions, such a configuration characterizes the spectral abscissa corresponding to the studied equation. A new stability criterion is proposed. This criterion extends recent results in factorizing quasipolynomial functions. The applicative potential of the proposed method is illustrated through the stabilization of coupled oscillators. [ABSTRACT FROM AUTHOR]