Algebraic Riccati equation

The Algebraic Riccati Equation (ARE) is a type of matrix equation that arises in various fields, including control theory, especially in linear quadratic optimal control problems. The general form of the Algebraic Riccati Equation is: \[ A^T X + X A - X B R^{-1} B^T X + Q = 0 \] where: - \( X \) is the unknown symmetric matrix we are trying to solve for.