TABLE OF CONTENTS James F Whidborne
Abstract. Control system design methods based on 
? theory are able to produce controllers that are both robust to model uncertainty and that have good performance. Furthermore, the method is applicable to multivariable systems. However, specifications for control system designs are rarely expressed explicitly in terms of the 
?-norm. Thus it is often not clear how to choose the weighting functions required in 
?-based design in order to meet the specifications. By posing the problem using the principle of inequalities (PoI), a method of inequalities (MoI) is proposed that can overcome some of the limitations of 
?-based control design. The efficacy of the method is demonstrated by a case study of the control of a distillation column.
Over the last two decades, there have been very significant developments in the analysis of robustness for control systems and a parallel development in methods for synthesising robust controllers. One of the better known approaches is based on 
? theory. The 
?-norm of a single-input single-output (SISO) transfer function is essentially the maximum magnitude of the frequency response. Control design using 
? theory is based on minimising the 
?-norm of some input-output transfer function(s). It can be easily shown that by making certain 
?-norms sufficiently small, robust stability can be guaranteed.
A number of relatively simple algorithms have been developed for synthesising 
?-optimal and sub-optimal controllers (Zhou et al, 1996; Skogestad and Postlethwaite, 1996); these are readily...
