Vol.3, No 15, 2003 pp.1017-1031
UDC 621.3.016.352
Invited Paper

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LYAPUNOV AND NON-LYAPUNOV STABILTY THEORY:
LINEAR AUTONOMOUS AND NON-AUTONOMOUS
SINGULAR SYSTEMS
Dragutin Lj. Debeljković
Faculty of Mechanical Engineering, Dept. of Control Engineering,
University of Belgrade, 27. marta 80, 11000 Belgrade, Serbia and Montenegro
E-mail: ddebeljkovic@mas.bg.ac.yu

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Abstract. Singular systems are those in which the dynamics are governed by a combination of algebraic and differential equations. The complex nature of singular systems causes many difficulties in the analytical and numerical studies of such systems, particularly when there is a need for their control. In that sense the question of their stability deserves great attention. A particular class of these systems operates in free as well as in forced regime. A brief survey of the results concerning their stability in the sense of Lyapunov and finite and practical stability are presented as the basis for their high quality dynamical investigation.
Key words: Singular systems, Lyapunov stability, Finite and Practical Stabilty

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TEORIJA LJAPUNOVLJEVE I NELJAPUNOVLJEVE STABILNOSTI: LINEARNI AUTONOMNI I NEAUTONOMNI SINGULARNI SISTEMI Singularni sistemi su oni sistemi čija dinamika zadovoljava sistem kombinovanih algebarskih i diferencijalnih jednačina. Složena priroda singularnih sistema je uzrok mnogih teškoća u analitičkim i numeričkim studiranjima takvih sistema, posebno kada je neophodno upravljanje. U tom smislu pitanje njihove stabilnosti privlači posebnu pažnju. Posebna klasa tih sistema se nalazi kako u slobodnom tako i u prinudnom režimu. Kratak pregled tih rezultata koji se tiču njihove stabilnosti u smislu Ljapunovljeve konačne i praktične stabilnosti predstavljaju osnovu za njihovu bolju kvalitativnu dinamički analizu.
Ključne reči: singularni sistemi, Ljapunovljeva stabilnost, konačna i praktična stabilnost