Positive Real And Dissipative Analysis And Control Of Uncertain Singular System

Singular system is a kind of dynamics of more general form compared with standard state-space systems. The theory of singular system, has been developed extensively since1970s, and becomes an independent branch of modern control theory. Enthusiasm has been poured into the study of singular system, and consequently a large number of research findings have been acquired. In practical systems, some uncertain parameters would emerge on account of all forms of unavoidable factors. Therefore, the results related to uncertain singular systems deserve more interests and attention of specialists.Positive real control property is an important performance of system. It plays an important role in the circuit, network and system stability. The implication of dissipative theory is that the energy consumption of a system is always less than the supply rate of the energy. The dissipativeness contains small gain and passivity as special cases. On the premise of system stability, Hm control aims to design a controller such that L2gain of the mapping from the disturbances to output is less than or equal to a prescribed level. The passivity, which takes the product of the input and output as the supply rate of energy, has been widely applied in many engineering fields, such as circuits and thermodynamic systems.This thesis focuses on the rubust positive real design of singular system with independent perturbation parameter uncertainty.Furthermore,we present the strictly positive real analysis and design of uncertain discrete-time systems. Also discussed the general robustness of the system is dissipative and positive real relationship.(1) The main background of the problem discussed in this thesis is introduced. Firstly, the structure characteristics and application background for singular systems are introduced. Then the development and recent progress are presented for singular systems. Furthermore, the significance and recent development of dissipative control and passive control problem for both normal and singular systems are summaried. The development and recent progress are presented for Positive real theory. Meanwhile, some relevant knowledge of both robust control theory and LMI is introduced. Finally, the main work of this thesis is listed.(2) Some basic knowledge of dissipative theory is introduced, including positive real property and dissipativeness for singular systems, together with common math tools. The definitions both frequently used and cited in this paper are emphasized, for most of the work in this thesis is on the basis of these definitions.(3) A class of uncertain singular perturbation parameter independent robust positive real control problem is considered. Basing on the theory of positive real lemma and using linear matrix inequalities, we achieve the design output feedback law robust stability and give the existence of conditions for the controller.(4) In contrast with the norm-bounded uncertainty, positive real uncertainty is considered in Chapter3. The uncertainty has roots in engineering and can be viewed as a generalization of the feedback gain. Conditions are characterized under the uncertain system which is robustly stable and strictly positive real. The robust positive real control of discrete-time systems is discussed here. Both state feedback and output feedback are considered.(5) The strictly dissipative analysis and control problems with quadratic supply rate as well as strictly passive analysis and control for discrete-time singular systems are considered. Equivalence between strict dissipativity and extended strictly positive realness is firstly established. By using the approach of LMI, necessary and sufficient conditions are given for discrete-time singular systems to be strictly dissipative, and the conditions of the strict LMIs are mainly derived.(6) A summary of this paper is given. At the same time, we give an expectation for the future work.