μ-Synthesis

Abstract

We have reviewed a general framework for control system analysis and synthesis. The structured singular value μ arose from the stability analysis of a more general type of systems, namely linear fractional transformations. This permits us to tackle formally the robust performance paradigm. To overcome the often reported difficulties in the lack of guidance in the weighting function selection during the design we have provided a simple and illustrative example which contains all ingredients and steps that should be carried out in analyzing such a design problem. Hopefully, we have succeeded in clarifying that a good design is a matter of balancing requirements. We might say that μ is the tool to guide us in finding the required trade-offs between performance and robustness. It places the challenge on the side of the practicing engineer. To be successful in improving the behaviour of complex systems he will have to quantify his specifications and he will have to rely continuously on a better and deeper system knowledge. The paradigm is no longer controller design, but specification design.