Troubleshooting for state-space H∞ design

Doyle/Glover´s state-space solution is widely accepted as an efficient and reliable means of testing feasibility of an H_∞. design and of generating an adequate controller. Yet, this simple solution lacks full generality and its inherent limitations may cause numerical difficulties or even failure of standard algorithms. This paper attempts an inventory of such shortcomings. Several sources of difficulties are identified: specializing assumptions of the approach, numerical sensitivity of the algorithms, particular choice of controller. The primary objective is to help users identifying and avoiding the main pitfalls of current state-space techniques for H_∞, design. The discussion is therefore application-oriented and illustrated by a few examples.