Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions

@article{Henrion2011InnerAF,
  title={Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions},
  author={Didier Henrion and Jean B. Lasserre},
  journal={IEEE Transactions on Automatic Control},
  year={2011},
  volume={57},
  pages={1456-1467}
}
Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modeled by parametrized polynomial matrix inequalities (PMIs). These feasibility sets are typically nonconvex. Given a parametrized PMI set, we provide a hierarchy of linear matrix inequality (LMI) problems whose optimal solutions generate inner approximations modeled by a single polynomial superlevel set. Those inner approximations… CONTINUE READING

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