The convergence analysis of an accelerated iteration for solving algebraic Riccati equations

The discrete-time algebraic Riccati equation (DARE) have extensive applications in optimal control problems . We provide new theoretical supports to the stability properties of solutions DARE and reduce convergence conditions under which accelerated fixed-point iteration (AFPI) can be applied compute numerical DARE. In particular, we verify that AFPI is R-superlinear when spectral radius closed-loop matrix greater than 1, shown by mild assumption only using primary theories Numerical examples are illustrate consistency effectiveness our results.