H~∞ Control And Dissipative Control Of Symmetric Systems

In recent years, considerable efforts have been devoted to the study of dynamic delayed systems and fuzzy systems due to their theoretical and practical importance in the study of various engineering, communication, biological, and chemical systems. The paper discusses stabilization, H∞control, and quadratic dissipative analysis of several classes of symmetric systems.The main contributions of this paper are as follows:In chapter 1, we introduce the research background and present results.In chapter 2, we studied H∞control analysis, the output feedback stabilization, and the output feedback H∞control synthesis problems for a class of state-space delayed symmetric system. New results on an explicit expression of the H∞control norm are obtained by choosing a sufficient condition of the H∞control of the delayed symmetric system. The output feedback stabilization and the output feedback H∞control synthesis performance analysis are also discussed.In chapter 3, we address the problem of dissipative control for a class of state-space delayed symmetric system. First, we give concepts of related dissipative analysis. Secondly, applying the Lyapunov function theory and linear matrix inequalities, some sufficient conditions of the mixed H∞and positive real criterion of the class of delayed symmetric system are established. Finally, the output feedback mixed H∞and positive real performance problem is also presented.In chapter 4, the H∞control analysis, the output feedback stabilization, and the output feedback H∞control synthesis problems for a class of state-space fuzzy symmetric system are discussed and new results on the fuzzy symmetric system are given.