Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F10%3A00172903" target="_blank" >RIV/68407700:21230/10:00172903 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities
Original language description
Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem that can be solved (locally) with PENNON, an implementation of a penalty and augmented Lagrangian method. Typically, Hermite SOF PMI problems are badly scaled and experiments reveal that this has a negative impact on the overall performance of the solver. In this note werecall the algebraic interpretation of Hermite's quadratic form as a particular Be´zoutian and we use results on polynomial interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an alternative to the conventional power basis. Numerical experiments on benchmark problem instances show the improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behaviour of PENNON.
Czech name
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Czech description
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Classification
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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Result continuities
Project
<a href="/en/project/GAP103%2F10%2F0628" target="_blank" >GAP103/10/0628: Semidefinite programming for nonlinear dynamical systems</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Control
ISSN
0020-7179
e-ISSN
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Volume of the periodical
83
Issue of the periodical within the volume
12
Country of publishing house
GB - UNITED KINGDOM
Number of pages
12
Pages from-to
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UT code for WoS article
000285354700008
EID of the result in the Scopus database
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