A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations (Q1763824)

Doubling algorithms for solving numerically the discrete algebraic Riccati equation (DARE) are based on a fixed point iteration \[ X_{k+1}= A^TX_k(I+GX_k)^{-1}A+H. \] The doubling algorithms produce the sequence \(\{X_{2^k}\}^\infty_{k= 1}\). In the reviewed paper, a doubling algorithm for the continuous algebraic Riccati equation (CARE) is proposed. Using the Cayley transform, CARE is transformed to DARE, with the Hamiltonian matrix being transformed into a symplectic matrix pair. Then a structure preserving doubling algorithm for DARE developed recently in: [\textit{E. K.-W. Chu}, \textit{H.-Y. Fan}, \textit{W.-W. Lin} and \textit{C.-S. Wang}, Int. J. Control. 77, No. 8, 767--788 (2004; Zbl 1061.93061)] is applied. A modified version of the structure preserving doubling algorithm for the case when the coefficients \(A\), \(G=H\) and \(H\) are symmetric and persymmetric, is developed as well. Extensive numerical results are presented showing the competitiveness of the structure preserving doubling algorithm for CARE.