Optimal reduced-order solution of the weakly coupled discrete Riccati equation

The optimal solution of the weakly coupled algebraic discrete Riccati equation is obtained in terms of a reduced-order continuous-type algebraic Riccati equation via the use of a bilinear transformation. The proposed method has a rate of convergence of O(ε² ) where ε represents a small coupling parameter. A real-world physical example (a chemical plant model) demonstrates the efficiency of the proposed method. Simulation results obtained using a package for a computer-aided control system are presented. For this specific real-world example, the algorithm perfectly matches the presented theory, since convergence, with an accuracy of 10^-4, is achieved after nine iterations (i.e., 0.68¹⁸=10^-4)