Closed-form solution of non-symmetric algebraic Riccati matrix equation

Abstract

In this work we obtain closed-form expression for the solution of non-symmetric algebraic Riccati equation (NARE), AX+XB+XCX=D,A,B,C,D∈ℂn×n, under some conditions on the matrices A,B,C and D. We show that the solution (real and complex) of this NARE is X=(A2+DC−A)C−1, where M is square root of matrix M. Finally this formula applied on some NAREs.