# 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} }

- Published in IEEE Transactions on…2011
DOI:10.1109/tac.2011.2178717

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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