Generalized system has more generalized form, and more precise description on the practical application. It is not only widespread in the aerospace, energy and other applications, but also the social production and our daily living closely. Therefore, study on descriptor linear systems is both theoretically and practically important.A big difference between a descriptor linear system and a conventional linear system is that the response of a descriptor linear system may contain impulsive terms. Such infinite jumps are obviously destructive as they could completely destroy the system instantaneously. In addition, in practice the state of a system is usually not directly available, so the state feedback control usually cannot be realized directly. In order to overcome this obstacle, we discuss the control problems of the singular system from state feedback and output feedback in the paper. At the same time, we notice that the controllers are designed based on proportional state feedback, proportional output feedback or dynamical output feedback, and there is not much attention to the controller design based on derivative feedback. Because of the specialization of derivative matrix of descriptor systems, some performances could not be realized by proportional feedback, but it could be realized by derivative feedback under some conditions, which implies the superiority of derivative feedback.Dissipative theory plays an important role in the stability research of control systems. Its implication is that there exists a non-negative energy function, which is also known as the storage function, such that the energy consumption of a control system is always less than the supply rate of the energy. Dissipative theory can contact some mathematical tools with physical phenomenon, and also give the description for control system from the viewpoint of energy described by input and output, what makes the study for the dissipation of generalized system is more important. It can be said that the passivity is an important part of the dissipation, and a further abstraction of the stability. It takes the product of the input and the output as the supply rate of the energy, and embodies the attenuation property of a system under bounded exogenous input.In response to these circumstances, this thesis focuses on the problems of impulse elimination and dissipative (and passive) control for singular systems, that is, to design feedback controllers for descriptor systems, which make the resulted closed-loop systems impulse-free and dissipative (passive). Firstly, the dissipative control problems and passive control problems for singular systems with impulse mode are discussed. The conditions of impulse dissipative and impulse passive for singular systems are given by LMI, from two aspects of state feedback and output feedback respectively, and the state feedback controller and output feedback controller are designed. By exemplifying, the feasibility of the theorem and four controllers designed is verified.Then linear systems with derivative input are equivalent transformed from the descriptor systems, by the first restricted equivalent transformation, and we analysis the dissipation of these systems. On this basis, the problem of proportional and derivative output feedback control for singular systems is investigated. Under the state space, we obtain the LMI design conditions of two impulse dissipative proportional and derivative feedback controller and two impulse passive proportional and derivative feedback controller, and the controllers make the closed-loop systems impulse-free and dissipative (or passive). After giving the design methods of controllers and proving the theorems, we provide numerical examples whose results demonstrate the validity and effectiveness of the proposed method.At last, a summary of this paper is given. At the same time, we give an expectation for the future work. |