The robustness of feedback systems with bounded complexity controllers

H_∞ methods for the analysis and design of robust feedback control systems have sometimes been criticized for an apparent conservatism. However, recent results have shown that they can provide the least conservative results possible under a particular set of assumptions. For example, a ball in the v-gap metric is the largest set of plants that can be guaranteed to be stabilized a priori by a controller known only to satisfy a bound on the induced norm of a particular closed-loop operator. Nevertheless, there are examples of uncertainty which, whilst large when measured by the v-gap metric, would be regarded as relatively benign by an experienced designer of control systems. The present paper examines the possibility that in arriving at this judgment, such a designer is implicitly using the knowledge that he will always choose the least complex controller necessary to do the job. It is shown that, given an appropriate bound on the complexity of the controller, significantly stronger a priori robustness results can be obtained