Original title:
Řízení lineárních systémů
Translated title:
Control of linear systems
Authors:
Cesneková, Ivana ; Milota, Jaroslav (advisor) ; Honzík, Petr (referee) Document type: Bachelor's theses
Year:
2012
Language:
slo Abstract:
[eng][cze] The aim of this work is to look into the theory of linear systems via population model represented by partial differential equations with boundary and initial condition. Special attention is devoted to the strongly continuous semig- roups on a complex Banach space. For this purpose, the notion of a homogeneous and inhomogeneous Cauchy problem is introduced and we solve our model in this abstract formulation. The system behaviour is based on properties of the resolvent set and spectrum. Controllability question limits to solve the uniformly exponen- tially stability and the exponentially stabilizability. The point of this problem is in the case of the unstability to show exponencially stability of the system by using feedback. Keywords: control, differential equations, stability, controllability 1Ciel'om tejto práce je nahliadnut' do teórie lineárnych systémov prostredníctvom populačného modela reprezentovaným parciálnou diferenciálnou rovnicou s okrajovou a počiatočnou podmienkou. Špeciálnu pozornot' venujeme silno spojitým semigrupám na Banachovom priestore. Za týmto účelom uvedie- me pojem homogénneho a nehomogénneho Cauchyovho problému a riešime daný populačný model v tejto abstraktnej formulácii. Správanie systému riešime na základe vlastností spektrálnej a rezolventnej množiny. Obecne otázku kontrolo- vatel'nosti obmedzíme na otázku uniformnej exponenciálnej stability a stabilizo- vatel'nosti. Snahou tohto problému, je v prípade nestability systému pomocou zpätnej väzby zaručit' stabilitu systému. Klíčová slova: kontrola, diferenciálne rovnice, stabilita, kontrolovatel'nost' 1
Keywords:
control; controllability; differential equations; stability; diferenciální rovnice; kontrolovatelnost; regulace; stabilita
Institution: Charles University Faculties (theses)
(web)
Document availability information: Available in the Charles University Digital Repository. Original record: http://hdl.handle.net/20.500.11956/40277