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 T XE   =   A T XA   -  ( A T XB ...+ C TS )( R   +   B T XB ) -1 ( B T XA   +   S TC )  +   C T QC . 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. [ABSTRACT FROM AUTHOR]