Control Theory And Application For Nonlinear Differential Algebraic Systems

Since the concept of differential algebraic system was put forward by Rosenbrock in the early 1970s, it has attracted many researchers' interests for its wide application in the fields of science and technology. In recent years, it has been found that many problems are modeled by differential algebraic system, such as electrical circuits, some population growth models, computer aided design and economics.Passive concept comes from physical systems. It takes the product of the input and the output as the supply rate of the energy, which embodies the attenuation property of a system under bounded input. In fact, the stabilization theory based on Lyapunov function can also be explained in view of the passivity. So the relationship between the passivity and the stability is as close as lips and teeth.Research of bilinear singular systems is still on the initial and developmental stage. Because bilinear singular systems contain nonlinear item, its research is more difficult than that of linear singular systems. So far, research of bilinear singular systems is still less.This thesis focuses on the passivity for a class of differential algebraic systems and stability for bilinear singular systems. The main content may be summarized as follows:(1) The passive control problems are investigated for a class of nonlinear differential algebraic systems and linear singular systems. A necessary and sufficient condition of passivation is given by making use of the methods similar to differential geometry and differential geometry methods respectively. By concretizing storage function and utilizing linear matrix inequalities, the sufficient condition of passivation for linear singular systems is deduced.(2) The existing condition and design of stabilizing controller for a bilinear...