Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F12%3A00193378" target="_blank" >RIV/68407700:21230/12:00193378 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1109/TAC.2011.2178717" target="_blank" >http://dx.doi.org/10.1109/TAC.2011.2178717</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TAC.2011.2178717" target="_blank" >10.1109/TAC.2011.2178717</a>

Result language
angličtina
Original language name
Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions
Original language description
Following a polynomial approach, many robust fixedorder 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 converge ina well-defined analytic sense to the nonconvex original feasible set, with asymptotically vanishing conservatism. One may also impose the hierarchy of inner approximations to be nested or convex. In the latter case, they do not converge any more to the feasible set, but they can be used in a convex optimization framework at the price of some conservatism. Finally, we show that the specific geometry of nonconvex polynomial stability regions can be exploited to improve convergence of the h
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BC - Theory and management systems
OECD FORD branch
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Project
<a href="/en/project/GAP103%2F10%2F0628" target="_blank" >GAP103/10/0628: Semidefinite programming for nonlinear dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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