Dynamical analysis of particular classes of linear time-delay singular control systems defined over finite and infinite time interval

In this thesis the problems of dynamical analysis of particular class of singular control systems with time delays are considered, as well as their behavior on finite and infinite time intervals. Emphasis has been put on the peculiar properties of singular ad descriptor systems, concerning the existence and uniqueness of the solutions, the problems of impulsive behavior, consistent initial conditions and causality of the system itself. On overview of the modern stability frameworks has been presented, starting from the classical Lyapunov ideas and extending through so called non-lyapunov concepts: finite time stability and practical stability in particular. A historical overview of ideas, concepts and results has been presented and the key contributions have been highlighted through key papers from the modern literature. This dissertation follows two main lines of research: the descriptive approach and the LMI (linear matrix inequalities) methodology, the latter being known to reduce control tasks to convex optimization problems, thus making them easily solvable by numerical computation. New results are presented. A new approach, based on lyapunov-like functions, is used in order to establish new sufficient conditions of practical and finite time interval stability of a particular class of singular time delay systems. Another new result is based on the modern LMI approach and gives new sufficient conditions for finite time stability. The obtained results are numerically verified and have great practical value, as they are easy to compute and less restrictive and conservative than their predecessors. U disertaciji su razmatrani problemi dinamičke analize posebnih klasa singularnih sistema sa čistim vremenskim kašnjenjem prisutnim u stanju sistema, kao i njihovo ponašanje na konačnom i beskonačnom vremenskom intervalu. Pružen je presek savremenih koncepata stabilnosti, prednosti jednih nad drugima i posebno su obrađeni tzv neljapunovski koncepti: stabilnost na konačnom vremenskom intervalu i koncept praktične stabilnosti. Nadograđene su osnovne definicije stabilnosti. Iscrpno je izložen hronološki sistematičan pregled osnovnih koncepata stabilnosti, polazeći od ljapunovske metodologije, kao osnove na kojoj se zasniva dinamička analiza sistema. Ukazano je na istorijski razvoj i nastanak ideja i rezultata u ovoj oblasti i na taj način su izvedene i smernice daljih istraživanja otvorenih problema. U disertaciji su sistemi tretirani sa stanovišta dva savremena p