A generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations

In Chu et al. (2004), an efficient structure-preserving doubling algorithm (SDA) was proposed for the solution of discrete-time algebraic Riccati equations (DAREs). In this paper, we generalize the SDA to the G-SDA, for the generalized DARE: E^TXE = A^TXA - (A^TXB + C^TS)(R + B^TXB)^-1(B^TXA + S^TC) + C ^TQC. Using Cayley transformation twice, we transform the generalized DARE to a DARE in a standard symplectic form without any explicit inversions of (possibly ill-conditioned) R and E. The SDA can then be applied. Selected numerical examples illustrate that the G-SDA is efficient, out-performing other algorithms.