Robust Stability For Several Classes Of Systems With Time-varying Delays

In this paper, we study asymptotic stability, robust stability, absolute stabilityand robust absolute stability for several classes of systems with time-varying de-lays, and obtain su?cient conditions on relevant stability. The whole paper consistsof six parts, whose content and structure are shown as follows.In the first chapter, we introduce the background and research methods ofrobust stability, and the main works are also listed in this chapter.In the second chapter, it is given the basic notations of Lyapunov stabil-ity theories, the main theorems of Lyapunov stability theories and the correlateknowledge of linear matrix inequalities.In the third chapter, we study asymptotic stability for nominal single systemswith time-varying delays and robust stability for uncertain systems, and obtainsu?cient conditions on relevant stability. Further, we expand the conditions ofrobust stability of uncertain systems by means of uncertain conditions and Schurcomplement lemma.In the fourth chapter, by means of constructing Lyapunov function, combinedwith linear matrix inequalities, we discuss absolute stability for nominal Luriesingle direct control systems with time-invariable delays and time-varying delays,and robust absolute stability of uncertain systems. We gain su?cient conditionson those stability.In the fifth chapter, we discuss absolute stability for nominal Lurie singleindirect control systems with time-invariable delays and time-varying delays firstly,and obtain distinguishing conditions of the stability. Afterward, we discuss robustabsolute stability of uncertain Lurie single, and gain distinguishing conditions onthose stability.In the six chapter, we study robust absolute stability for multiple nonlinearinterval Lurie system with time-varying delays. Based on the knowledge of inter-val matrix and Lyapunov stability theory, we obtain distinguishing conditions onrobust absolute stability.