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Statements

Subject Item
n2:RIV%2F68407700%3A21230%2F08%3A03145471%21RIV09-MSM-21230___
rdf:type
n19:Vysledek skos:Concept
dcterms:description
The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however that quite often for benchmark problem instances, the set of stabilizing controllers seems to be convex. In this note we use elementary techniques from real algebraic geometry (resultants and B´ezoutian matrices) to explain this phenomenon. As a byproduct, we derive a convex linear matrix inequality (LMI) formulation of two-parameter fixed-order controller design problem, when possible. The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however that quite often for benchmark problem instances, the set of stabilizing controllers seems to be convex. In this note we use elementary techniques from real algebraic geometry (resultants and B´ezoutian matrices) to explain this phenomenon. As a byproduct, we derive a convex linear matrix inequality (LMI) formulation of two-parameter fixed-order controller design problem, when possible. Geometrie roviny a konvexita polynomiálních oblastí stability
dcterms:title
Geometrie roviny a konvexita polynomiálních oblastí stability Plane geometry and convexity of polynomial stability regions Plane geometry and convexity of polynomial stability regions
skos:prefLabel
Geometrie roviny a konvexita polynomiálních oblastí stability Plane geometry and convexity of polynomial stability regions Plane geometry and convexity of polynomial stability regions
skos:notation
RIV/68407700:21230/08:03145471!RIV09-MSM-21230___
n3:aktivita
n9:Z n9:P
n3:aktivity
P(GA102/08/0186), Z(MSM6840770038)
n3:dodaniDat
n15:2009
n3:domaciTvurceVysledku
n10:9676708 n10:6204821
n3:druhVysledku
n21:D
n3:duvernostUdaju
n11:S
n3:entitaPredkladatele
n8:predkladatel
n3:idSjednocenehoVysledku
386732
n3:idVysledku
RIV/68407700:21230/08:03145471
n3:jazykVysledku
n4:eng
n3:klicovaSlova
control theory; convexity; resultants
n3:klicoveSlovo
n5:resultants n5:control%20theory n5:convexity
n3:kontrolniKodProRIV
[C1371E583392]
n3:mistoKonaniAkce
Hagenberg
n3:mistoVydani
New York
n3:nazevZdroje
Proceedings of the International Symposium on Symbolic and Algebraic Computations
n3:obor
n17:BC
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:projekt
n7:GA102%2F08%2F0186
n3:rokUplatneniVysledku
n15:2008
n3:tvurceVysledku
Henrion, Didier Šebek, Michael
n3:typAkce
n6:WRD
n3:zahajeniAkce
2008-07-20+02:00
n3:zamer
n20:MSM6840770038
s:numberOfPages
6
n12:hasPublisher
Association of Computing Machinery
n22:isbn
978-1-59593-904-3
n13:organizacniJednotka
21230