Existence of The Solution to The Quadratic Bilinear Equation Arising from A Class of Quadratic Dynamical Systems

A quadratic dynamical system with practical applications is taken into considered. This system is transformed into a new bilinear system with Hadamard products by means of the implicit matrix structure. The corresponding quadratic bilinear equation is subsequently established via the Volterra series. Under proper conditions the existence of the solution to the equation is proved by using a fixed-point iteration.