On applications of Schauderʼs fixed-point theorem for the solution of the non-symmetric algebraic Riccati equation

In this article, we give sufficient conditions for the existence of contractive solutions for the Non-Symmetric Algebraic Riccati Equation. The conditions are given in terms of the matrix of the coefficients - only. We also provide sufficient conditions for unique contractive solution (which is a unique minimal-norm solution). The results are generalized to contractive solutions with respect to generalized unit matrix balls.