Stability of singular time-delay systems in the sense of non-Lyapunov: classical and modern approach/NE-liapunovska stabilnost singularnih sistema sa cistim vremenskim kasnjenjem: klasican i savremen pristup

• Published in: Hemijska industrija 2013-03, Vol.67 (2), p.193
• Main Authors: Debeljkovic, Dragutin Lj, Stojanovic, Sreten B, Aleksendric, Marko S
• Format: Article
• Language: English
• ISSN: 0367-598X
• DOI: 10.2298/HEMIND120403061D

This paper provides sufficient conditions for both practical stability and finite-time stability of linear singular continuous time-delay systems, which can be mathematically described as [E.sub.[??]](t) = [A.sub.0]x(t) + [A.sub.1]x(t - [tau]) Considering a finite-time stability concept, new delay independent and delay dependent conditions have been derived using the approach based on the Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to have the properties of positivity in the whole state space and negative derivatives along the system trajectories. When the practical stability has been analyzed, the above mentioned approach was combined and supported by the classical Lyapunov technique to guarantee the attractivity property of the system behavior. Moreover, a linear matrix inequality (LMI) approach has been applied in order to get less conservative conditions. Keywords: singular system, time-delay, finite-time stability, attractive practical stability, linear matrix inequality. U ovom radu izvedeni su dovoljni uslovi kako prakticne tako i stabilnosti na konacnom vremenskom intervalu linearnih singularnih sistema sa cistim vremenskim kasnjenjem, koji se u matematickom smislu mogu opisati sledecim modelom: [E.sub.[??]](t) = [A.sub.0]x(t) + [A.sub.1]x(t - [tau]) Razmatrajuci koncept stabilnosti na konacnom vremenskom intervalu, izvedeni su novi, dovoljni uslovi stabilnosti, koji ne uzimaju i koji uzimaju u obzir iznos cisto vremenskog kasnjenja, koristeci prilaz koji se zasniva na koriscenju kvazi Ljapunovljevih funkcija i njihovih osobina na podprostoru konzistentnih pocetnih uslova. Ove funkcije ne moraju da budu pozitivno odredene u celom prostoru stanja, kao sto i njihovi izvodi duz trajektorija sistema ne moraju da budu negativno odredene funkcije. Kada je razmatran koncept prakticne stabilnosti, prethodno pomenuti prilaz kombinovan je sa klasicnim Ljapunovskom tehnikom kako bi se obezbedila atraktivna (privlacna) prakticna stabilnost razmatranog dinamickog ponasanja sistema. Stavise, prilaz sa stanovista LMI (eng. linear matrix inequality) metoda je takode primenjen sa ciljem da se oslabe neki od ogranicavajucih uslova iz prethodnih rezultata. Kljucne reci: Singularni sistem * Vremensko kasnjenje * Stabilnost na konacnom vremenskom intervalu * Atraktivna prakticna stabilnost * Linearna matricna nejednakost Available online at the Journal website: