Numerical Calculation for Discretization of Continuous Quadratic Performance Index

Abstract

A new procedure of numerical calculation to discretize a quadratic performance index denned for a linear time-invariant continuous system is proposed. The procedure is based on the Padé approximation with scaling and repeated squaring. Theoretical bounds of truncation errors involved in the resulting discretized weighting matrices are provided in terms of the maximum singular value norm for the proposed procedure. It is also shown that the paper by Van Loan which proposed another procedure of numerical calculation for the same problem contains some errors and a certain modification is required for his procedure. Numerical examples show that the new procedure is superior to the old one (of the modified version) from the viewpoint of accuracy, efficiency, and reliability.