Newton’s method for coupled continuous-time algebraic Riccati equations

We seek the solution of the coupled continuous-time algebraic Riccati equations, arising in the optimal control of Markovian jump linear systems. Newton’s method is applied to construct the solution, under a mild and natural stabilizability assumption, leading to some coupled Lyapunov equations. Iterative methods of \(O(n^3)\) $O(n^3)$ computational complexity for the coupled Lyapunov equations and the corresponding Newton’s methods for the coupled continuous-time algebraic Riccati equations are analyzed. Illustrative examples are presented.