Design Of Non-fragile Filter For Uncertain Discrete-time Systems

As one of the most pivotal problem in control area and signal processing, filtering has important theoretical and engineering significance. Filtering has attracted recurring interest since Kalman proposed the optimal filtering theory and successfully applied in aerospace field. The well-known Kalman filtering is based on accurate mathematical models and assumes the a priori information on the external noises to be precisely known. To overcome these defects, robust filtering has been presented. However, further study found that limitations of computer word length in the digital implementation of control systems and quantization error in the limited bandwidth communication channels for feedback control may cause filter parameters to have small variation. This usually leads to the reduction of filtering performance and even disappear completely.In practice, the filter often contains uncertain factors, so the non-fragile and quantized filtering problem have been concerned by many scholars.This paper considers the problem of non-fragile filter design for uncertain discrete-time system with output quantization and non-fragile filter with randomly occurring gain variations. Meanwhile, some control performance indicators have been considered, that is, H∞ performance and H2 performance. A sufficient condition of non-fragile H∞ filter with randomly occurring gain variations is presented. The difficulty of this paper is that three types of uncertain have been considered in the process of filter design, that is, the uncertain in system, the uncertain in non-fragile filter and the quantization error uncertain; non-fragile filter consider the influence of the performance of system. Popularly, the design thinking can be conclude as follow: based on Lyapunov stability theory and by using effective matrix transformation techniques and relaxed lemmas some slack matrix variables have been introduced, a sufficient condition is presented in terms of linear matrix inequalities(LMIs) for such three kind of non-fragile filters exist. The main results are provided to demonstrate the effectiveness of the proposed approach in every chapter.At last, the results of the dissertation are summarized and further research topics are pointed out.