Numerical Computation for Solving Algebraic Riccati Equations of Weakly Coupled Systems

摘要

In this paper, an algorithm for solving the algebraic Riccati equation (ARE) that has an indefinite sign quadratic term related to weakly coupled large-scale systems is investigated. A novel contribution is that a new iterative algorithm is derived by combining Newton's method and the fixed point algorithm. As a result, for sufficiently small ε, we can obtain an ARE solution with a quadratic convergence rate. Moreover, it is possible to calculate the ARE solution for the same dimension of each subsystem. As another important feature, an algorithm for solving the filter ARE is also discussed. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example is given.