Historical perspectives of the Riccati equations
Résumé
All the equations and inequalities, that are algebraic or differential are nowadays called of Riccati type if they consist of a constant, linear ones and quadratic terms in the variables. Such nonlinear mathematical tools are of crucial importance because they are based on the simplest class of nonlinear polynomial: the polynomials of degree two. Since their introduction at the end of the seventeenth century, they have been studied intensively by renown mathematicians with numerous approaches underlying all the facets of their richness. Their field of applications is widespread especially in control system theory. This survey offers historical perspectives of the Riccati equations: the prehistory of Riccati equations, the crucial work of Jacopo F. Riccati based on the variable separable technique, the important approach of the continued fractions and finally the developments from the Enlightenment until the applications in control system theory.