An iterative algorithm for the solution of the discrete-time algebraic Riccati equation

Abstract

The discrete-time algebraic Riccati equation is solved in this study by an iterative algorithm for the square root of a squared Hamiltonian matrix, which is obtained from the S + −1 transformation of the symplectic pencil associated with the Riccati equation. The symplectic Givens and n × n block-diagonal orthogonal transformations are used before the iterative process so that the iteration is structure-preserving and can achieve on average 60% reduction of computation time compared with the QZ algorithm. A formal analysis for roundoff errors and some numerical examples are also given.