New doubling algorithm for the discrete periodic Riccati Equation

The periodic Riccati equation that results from periodic state space models plays an important role in many fields of mathematics, science, and engineering. In most applications, it is essential that the solution to the Riccati equation be obtained in the shortest possible time. Such a computationally effective doubling algorithm that solves the discrete periodic Riccati equation is proposed in this paper. Moreover, the memory requirements and the calculation burden needed for the sequential implementation of the proposed algorithm are established, and compared to the memory requirements and the calculation burden needed for the sequential implementation of classical algorithms. The basic conclusion of the above comparison is that the calculation time required to solve the periodic Riccati equation using the classical algorithms is in general much greater than the calculation time required to solve the periodic Riccati equation by using the proposed algorithm. Finally, the numerical behavior of the proposed algorithm is tested through simulation examples. It is established that the proposed algorithm is fast, computationally efficient, and numerically stable, and possesses very good parallelism efficiency.