A quadratic bilinear equation arising from the quadratic dynamical system

Abstract

A quadratic dynamical system with practical applications is taken into consideration. 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. Numerical experiments verify the proposed theory of the solution.

Keywords

• quadratic bilinear system
• kronecker product
• hadamard product
• existence of the solution
• fixed-point iteration.