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 + S-1 transformation of the symplectic pencil associated with the Riccati equation. The symplectic Givens and n X 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.[[fileno]]2010223010066[[department]]數學