On the solution of a class of algebraic matrix Riccati equation

We consider the algebraic matrix Riccati equation of control theory arising with a scalar control. It is shown that, if the Riccati equation is taken in phase-variable canonical form, the solution may be effected by solving a scalar polynomial equation whose degree is that of the unknown matrix. The resolution of the problem involves only elementary algebraic operations on the solution of the scalar polynomial equation. An illustrative numerical example is given.