On the Gap Between the Complex Structured Singular Value and Its Convex Upper Bound
SIAM JOURNAL ON CONTROL AND OPTIMIZATION(2006)
Abstract
The gap between the complex structured singular value of a complex matrix $M$ and its convex upper bound is considered. New necessary and sufficient conditions for the existence of the gap are derived. It is shown that determining whether there exists such a gap is as difficult as evaluating a structured singular value of a reduced rank matrix (whose rank is equal to the multiplicity of the largest singular value of $M$). Furthermore, if an upper bound on this reduced rank problem can be obtained, it is shown that this provides an upper bound on the original problem that is lower than the convex relaxation upper bound. An example that illustrates our procedure is given. We also give the solution of several structured-approximation problems of independent interest.
MoreTranslated text
Key words
reduced rank problem,μ-analysis,complex matrix,distance to singularity,robust control,structured uncertainty,largest singular value,convex relaxation,structured-approximation problem,structured singular value,complex structured singular value,toeplitz matrices,independent interest,convex upper bound,reduced rank matrix,original problem,complex structure,upper bound,singular value
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined