Mathematical Problems in Engineering
Volume 6 (2000), Issue 2-3, Pages 125-144

Synthesis of fixed-architecture, robust H2 and H controllers

Emmanuel G. Collins Jr. and Debashis Sadhukhan

Department of Mechanical Engineering, Florida A&M University – Florida State University, 2525 Pottsdamer Street, Tallahassee 32310-6046, FL, USA

Received 14 December 1998

Copyright © 2000 Emmanuel G. Collins and Debashis Sadhukhan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper discusses and compares the synthesis of fixed-architecture controllers that guarantee either robust H2 or H performance. The synthesis is accomplished by solving a Riccati equation feasibility problem resulting from mixed structured singular value theory with Popov multipliers. Whereas the algorithm for robust H2 performance had been previously implemented, a major contribution described in this paper is the implementation of the much more complex algorithm for robust H performance. Both robust H2 and H , controllers are designed for a benchmark problem and a comparison is made between the resulting controllers and control algorithms. It is found that the numerical algorithm for robust H performance is much more computationally intensive than that for robust H2 performance. Both controllers are found to have smaller bandwidth, lower control authority and to be less conservative than controllers obtained using complex structured singular value synthesis