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Statements

Subject Item
n2:RIV%2F68407700%3A21230%2F11%3A00185249%21RIV12-GA0-21230___
rdf:type
n7:Vysledek skos:Concept
dcterms: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 we recall the algebraic interpretation of Hermite's quadratic form as a particular Bezoutian 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 experi- ments on benchmark problem instances show the substantial improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behavior of PENNON. 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 we recall the algebraic interpretation of Hermite's quadratic form as a particular Bezoutian 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 experi- ments on benchmark problem instances show the substantial improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behavior of PENNON.
dcterms:title
Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities
skos:prefLabel
Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities
skos:notation
RIV/68407700:21230/11:00185249!RIV12-GA0-21230___
n7:predkladatel
n14:orjk%3A21230
n3:aktivita
n15:P
n3:aktivity
P(GAP103/10/0628)
n3:dodaniDat
n4:2012
n3:domaciTvurceVysledku
Henrion, Didier
n3:druhVysledku
n12:O
n3:duvernostUdaju
n9:S
n3:entitaPredkladatele
n16:predkladatel
n3:idSjednocenehoVysledku
201921
n3:idVysledku
RIV/68407700:21230/11:00185249
n3:jazykVysledku
n6:eng
n3:klicovaSlova
Static output feedback; Hermite stability criterion; Polynomial matrix inequality; Nonlinear semidefinite programming
n3:klicoveSlovo
n5:Hermite%20stability%20criterion n5:Polynomial%20matrix%20inequality n5:Nonlinear%20semidefinite%20programming n5:Static%20output%20feedback
n3:kontrolniKodProRIV
[C2B5CF38893E]
n3:obor
n13:BC
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n11:GAP103%2F10%2F0628
n3:rokUplatneniVysledku
n4:2011
n3:tvurceVysledku
Delibasi, A. Henrion, Didier
n17:organizacniJednotka
21230