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We say that a Hurwitz polynomialptis a Hadamardized polynomial if there are two Hurwitz polynomialsftandgtsuch thatf∗g=p, wheref∗gis the Hadamard product offandg. In this paper, we prove that the set of all Hadamardized Hurwitz polynomials is an open, unbounded, nonconvex, and arc-connected set. Furthermore, we give a result so that a fourth-degree Hurwitz interval polynomial is a Hadamardized polynomial family and we discuss an approach of differential topology in the study of the set of Hadamardized Hurwitz polynomials.

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

The main aim of this paper is to generate multistability from a type of unstable systems which have all their roots in the right half of the complex plane. For the realization of this, we use a system of linear differential equations that consists of two parameters. First we use an instability parameter to transform an unstable system to a type of system capable of generating attractors by means of a piecewise linear function. Then we use another bifurcation parameter to change from multiscroll attractors in a mono-stable state into several single-scroll atractors in multi-stable states.