Properties of a quadratic matrix equation and the solution of the continuous-time algebraic Riccati equation
The quadratic matrix equation \(X^2 - BX + C = 0\) is considered and its properties are emphasized. These properties are used to derive a new method for solving the algebraic Riccati equation (ARE). Then, using \textit{C. Van Loan's} idea [Linear Algebra Appl. 61, 233-251 (1984; Zbl 0565.65018)], an algorithm is given for the real ARE, consisting only of real operations and which takes account of special matrix structure. The advantages of the proposed algorithm are emphasized by applying it to some examples from a paper of \textit{A. J. Laub} [IEEE Trans. Autom. Control, AC-24, 913-921 (1979; Zbl 0424.65013)].
scientific article; zbMATH DE number 778239