Stabilization of finite dimensional control systems: a survey

Ludovic Rifford

Description

Stabilization of finite-dimensional control systems: a survey Ludovic Rifford Universite de Nice - Sophia Antipolis Ludovic Rifford Stabilization of finite-dimensional control systems

• control can


• stabilizing feedbacks


• globally asymptotically


• universite de nice


• finite-dimensional control


• let x˙


• lyapunov stability

Sujets

• Antipolis
• Universidad de Niza Sophia Antipolis
• Lyapunov stability

Informations

• Publié par: pefav
• Nombre de lectures: 7
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

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Universit´edeNice-SophiaAntipolis

Stabilization of finite-dimensional systems: a survey

control

Ludovic Rifford

Ppourlakhtteesfo ibilSdatnofoazitLudoifforvicRstsysemonlcoltrsnemanoitinfiid-e

which is globally asymptotically controllable, study the existence and regularity of stabilizing feedbacks.

f(O,0) = 0

Given a control system

with an equilibrium point

x=f(x,u) ˙

trolyconcalltotiyspmllayolabG assitIlGebotdi esyslabltems O∈ at ftMitwheolofiwolrpgnreposeit oballyAsymptoticlayloCtnorllbael tnocasiereht,M∈x Us)→,∞[0):(∙ l u rotArt efi:dtasirase each:Forvityacti ,0[:M→)∞ ,x x y )∙( u t→as Ly ∞.ndteoOst ehocrrsecuthahttrajectorpondingt monetsssobhriehg ofO,oodV eexither nhcaeroFhrobhgieStovunapy:itilab neushchtta x x u, t( controlcanbechosU∈x f nehtaehtevob dUooOsofhtuctiha lsysntroalcosionmineetd-fifinoionatizilabStrdffoRicivoduL .0≥t∀,V∈)

u∈U,

∈M,

x

smet

x˙ =f(x,u),

be a control system.

Let

Globaotitacllllayyspmbllaysesonycoltrsmet aehcF:rohtre∈x,Mconteisa (∙): rol usU→)∞,0[ttahthcuesrrcohegtinndpo trAttiactyvi nemosstsixeereht O,ofdVoorhboghei htnex f U∈ ahitcuthofOsoodUborheigh dnetOots,0[:M→)∞ x, y x∙) u ( jeraorct oFercanhbaliti:yapunovSt ast→∞. Ly enim-dtecoalonsitazilibainfifonoi

x∈M,u∈U,

It is said to beGlobally Asymptotically Controllableat O∈Mif the two following properties are satisfied:

slsytnor

Let

x˙ =f(x,u),

be a control system.

etsm beanoschsuenthchaehtevobtnocclor . LudovicRiffordSt ta x x u, t(∈),Vt∀0≥