Algebraic Riccati Equation: Hermitian and Definite Solutions

Abstract

Let A, B, and C be constant n × n matrices with entries in C, the field of complex numbers. Let B and C be hermitian, i.e., B = B* and C = C*, where an asterisk is used to denote the conjugate transpose of a matrix. The quadratic equation $$XA + A*X - XBX + C = 0$$ (3.1) for the n × n complex matrix X is called the algebraic Riccati equation.