Simplifying robust control designs of parametric uncertain systems using dimensional transformations

Robust control techniques have become more popular in the last decade because of their ability to construct a single controller suitable for a family of plants that are represented as a nominal plant with an uncertainty bounds. A typical challenge with robust control design is that, as the size of the uncertainty block gets bigger, the complexity of the control synthesis and resulting controller exponentially increases. Using a dimensional transformation method, this work shows that some robust control problems can be recast into an equivalent representation with a much smaller size of uncertainty block. This reduction potentially reduces the conservativeness and computational complexity of both H_∞/μ - synthesis methods. This method is demonstrated using the 1990 ACC benchmark problem.