Improvement of system order reduction via balancing using the method of singular perturbations

In this paper we first present several alternative techniques for system or der reduction based on system balancing by employing the method of singular perturbations. The techniques obtained have the same robustness accuracy e valuated with respect to the H-infinity norm of the reduced-order system as the two techniques existing in the control literature known as the direct truncation and balancing residualization methods. The newly proposed techni ques preserve the exact DC gain as the original system, and produce very go od to excellent accuracy at low and medium frequencies. We also present a s imple formula that fixes the DC gain for the direct truncation method. In t he second part of the paper we propose how to perform order-reduction of a balanced system using theory of singular perturbations that can produce ver y good accuracy at high frequencies, particularly for systems that have lig htly damped highly oscillatory modes. The result obtained for such kind of systems requires that the modes with higher Hankel singular values should b e neglected and those with smaller Hankel singular values should be retaine d. This is a counter-intuitive result in the spirit of H-infinity theory, b ut an intuitive result in the spirit of theory of singular perturbations. T he second part of the paper raises an important question about validity of the system robustness estimate based on the H-infinity norm for linear syst ems with lightly damped highly oscillatory modes. (C) 2001 Elsevier Science Ltd. All rights reserved.