H_∞ Filtering For Singular Systems

The filtering problem, which is concerned with estimating the state variables of a dynamic system based on the corrupted system output measurement data, has been widely studied, and has found many practical applications. One of the most popular ways to deal with this problem is the celebrated Kalman filtering approach, which generally provides an optimal estimation of the state variables in the sense that the covariance of the estimation error is minimized. It is noted that the Kalman filtering approach is based on the assumptions that the system under consideration has exactly known dynamics described by certain well-posed model, and its disturbances are stationary Gaussian noises with known statistics. In some applications, however, the noise sources may not be exactly known. Also, it has been shown that the standard Kalman filtering algorithm cannot guarantee satisfactory performance when there are parameter uncertainties in a system model, these limit the scope of applications of the Kalman filtering technique. In view of these, an alternative estimation method based on H1 filtering technique has been proposed recently. In recent years, a great deal of attention has been devoted to the study of H∞filtering for singular systems over the past decades. However, as the singular systems of its own specificity, it is very difficult to design the H∞filtering for singular systems. So, it has important practical significance to study the problem of the H∞filtering for singular systems and uncertain singular systems.In this thesis, a detailed analysis of the current situation of study on H∞filtering for singular systems and a discussion about the problems of H∞filtering for singular systems, uncertain singular systems and nonlinear singular systems are stressed. The main results in this thesis are as follows.Chapter 1 briefly introduces the problems in this paper, and gives the background about the research.Chapter 2 firstly introduces some basic definitions and common lemmas.Chapter 3 introduces some typical H∞filtering for singular systems.Chapter 4 considers the H∞filtering problem for uncertain singular system with time-delay. A sufficient condition for filtering is given, and we get a filtering designed method. By existing Matlab software, H∞filtering problem for singular system with time-delay can be easily designed.Chapter 5 considers the H∞filtering problem for nonlinea singular system. A sufficient condition for filtering is given, and we get a filtering designed method. By existing Matlab software, an illustrative example is presented to demonstrate the applicability of the proposed approach.Finally, a conclusion is given to summarize the thesis work.