Observers Design For Several Kinds Of Linear Singular Systems

In the design of singular systems, state feedback problems are very common. In order to achieve state feedback, all of the state information is needed. But in practical systems, what can be directly measured are outputs, not states. This causes the difficulty of state feedback in physical achievement. The superiority of state feedback and the difficulty of constructing state feedback are contradict, which can be solved by introducing state reconstruction or sate estimation. Taking reconstruction state or estimation state as feedback variables to construct state feedback means that achieving states in state feedback by a dynamic system named state observer. With the development of science and technology, state observers theory and design of singular systems are attached great importance and have gained extensive applications in such fields as practical engineering, science and technology, economics, biological, internet analysis, education and so on.This thesis investigates observers design problems about some categories of linear singular systems, including sufficient conditions of observers existing as well as concrete design of corresponding observers. The whole thesis includes three chapters as follows.Chapter 1 introduces the development of singular systems, research background and mathematical description of state observers. Preparing knowledge about observers design of linear singular systems is given in this chapter.Chapter 2 studies observers design of general linear singular systems. Sufficient conditions of observers existing are given respectively in accordance with the design of system function observers, descending order observers and whole order observers. Moreover, concrete design steps of corresponding observers are obtained by the method of linear matrix inequality (LMI). Then, numerical examples of the design are given, respectively.Chapter 3 discusses observers design of two categories of special singular systems. One category is observers design of linear singular systems including disturbed inputs. Another is observers design of singular systems including nonlinear feedback. This chapter mainly studies function observers design of these two categories of systems and gives sufficient conditions of observers existing. Furthermore, concrete design steps of corresponding observers are obtained by the method of linear matrix inequality (LMI) and numerical examples of the design are given, respectively. Conclusions analogous to those in chapter 2 are given on descending order observers and whole order observers of two categories of systems.