Performance improvement in computing the L-infinity norm of descriptor systems

Abstract

"Efficient and realible algorithms for finding the L-infinity norm for both continuous- and discrete-time descriptor systems have been recently developed. These algorithms exploit the underlying Hamiltonian or symplectic structure of the computational problem. The solver incorporating these advances has been extensively tested on large sets of control applications. Numerical results and comparisons illustrated the good performance and effectiveness of this solver. However, further investigations have shown that the performance can still be improved. The refinements performed include a better selection of the test frequencies used to find a lower bound for the L-infinity norm and of the tolerances for detecting the poles lying on the boundary of the stability domain, a better use of the computer memory hierarchy, an optimal workspace for computations, etc. Such refinements allowed not only to reduce the computing time, but also to improve the accuracy and reliability of the results. "