Study On Delay-dependent Robust Control Based On An Integral Inequality Approach

Time delays are frequently encountered in a variety of dynamic systems, and they are often sources of instability and degradation in control performance in control systems. So the study of dynamic control systems with delays is important both in theory and in practice, and has thus been of great interest to a large number of researchers for the last few decades. In particular, delay-dependent criteria, which employ information about the delay, have received much attention. A variety of model transformation approaches for designing them have been proposed and continue to appear from time to time in the literature. This dissertation clarifies the basic characteristics of these model transformation methods and presents a refined method, called the integral inequality approach (IIA), for analyzing the delay-dependent stability of systems with a time delay. Then, based on the new method, a number of synthesis problems (robust stabilization, H_∞ control, passive control, etc.) are investigated for various time-delay systems, including neutral systems, descriptor systems, and discrete-time systems.In this dissertation, some integral inequalities are first established. Then, integral inequalities are employed to analyze the delay-dependent stability of systems with a time-varying delay. Two types of time-delay are discussed: (I) continuous but not differential and (I) continuous and differential; and two classes of delay-dependent stability conditions, one for each type, are obtained. Moreover, the relationship between these two classes is also explained: when the delay is differential, if the upper bound on its derivative is less than one, the delay-dependent conditions for Type I are less conservative...