Robust Filtering For Discrete Markov Jump Systerm

Among many practical systems, due to the presence of environmental impact, the device loss and other factors, making the change of system parameters to produce uncertain system,therefore, Robust filtering for uncertain systems is important. Kalman filter is a well-known method of state estimation, which is widely used in systems , control theory and signal processing . But classic Kalman filter is based on a precise mathematical model, and the parameter uncertainties make it difficult to obtain an accurate model of the practical system.Therefore, robust filtering method is proposed to solve this problem. Furthermore, in order to solve the unknown statistical characteristics of the interferential noise in system, the H? filtering is proposed. When the system's model has uncertainty and characteristics of the interferential noise are difficult to calculate,the H? filtering is proposed. Robust H?filtering method is the H? norm,which cases from the interferential noise signal to the transfer function for the error system is all in uncertain ,to ensure that within a specified range.The reduced-order filter is designed to reduce the complexity and computational burden of the real-time filtering procession, the filter works to achieve significance. This paper was based on Lyapunov stability theory, used linear matrix inequality (LMI) for robust H? filtering research of Markovian jump system, and design full-order and reduced-order filterings. The considered systems are discrete-time Markovian jump systems, and contain uncertainty and time-varying delay. There is norm-bounded uncertainty. The system's modal can be described by discrete state Markovian process that system is based on Markovian chain is in limit space,.According to the transition probability, it can transfer from one state to the next.Firstly, it gave a brief description of the background, the development of filtering theory,current situation, and then summarized the theory of linear matrix inequalities, uncertainties and H? filtering problems. Finally, robust H? filtering of discrete-time Markov jump system was proposed in uncertain systems and time-dependent delay systems. Its purpose was to design a robust H? filtering for all admissible uncertainties. The filtering error system was asymptotically stable,and had a certain H? performance. According to the Matrix decomposition, it can get a new linear matrix inequality (LMI) of the filtering, and this method was extended to reduced-order filtering.