An Overview on D-stable Matrices

We give an overview on the main properties of D-stable matrices, i.e. of those square matrices $A$ for which the product DA is stable for any choice of the diagonal matrix D, with all positive diagonal elements. These matrices, introduced in economic analysis by Arrow and Mc Manus (1958), have found, besides applications in mathematical economics, applications also in other fields, such as mathematical ecology, population dynamics, the theory of electric circuits, analysis of neural networks, control theory and other questions.