Some computational results on size reduction inH∞ design

The authors explore the properties of the algebraic Riccati equation. New results on the rank of the solution to the algebraic Riccati equation are obtained and lead to an efficient algorithm for reducing the size of the antistable transfer function matrix in the model-matching problem. In the 1-block problem, the method is taken further to obtain explicit formulas for a minimal realization of the matrix. The approach is direct and numerically reliable as it is based almost entirely on orthogonal transformations