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

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 is an element of C-n Chi 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 = (root A(2) + DC - A)C-1, where root M is square root of matrix M. Finally this formula applied on some NAREs. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this work, a closed-form expression for the solution of the non-symmetric algebraic Riccati equation (NARE) is obtained, under certain conditions on the matrices involved. It is shown that the solution of this NARE is given by X = (root A(2) + DC - A)C-1, where root M denotes the square root of matrix M. The formula is then applied to some NAREs.