Robust H_∞ Filtering Of Linear Systems With Time Varying Delay And Its Application

Time delay phenomenon is widely exited in a variety of practical control system, if ignoring them in the process of system analysis and design, it may cause system performance degradation, even lead to serious system instability. In recent years, the H_∞filtering problem attracted more and more attention. In the actual control process, such as network control systems, biochemical reactions, and image processing, problems with uncertain parameters and H_∞filter design with time delay are often encountered, Therefore, the study of H_∞filtering problem has broad application prospects.Continuous and discrete systems robust H_∞filter design are studied respectively in this dissertation, as well as system mathematical modeling and robust H_∞design method. The main contents are as follows:Robust H_∞filtering analysis and synthesis problems are researched for continuous time-varying delay system. By means of the freedom matrix method and the Jensen integral inequality, ultimately sufficient conditions for system with H_∞performance are derived, the exiting conditions and parameters solving method of the formal system H_∞filters are given. Study results are compared with existing numerical examples.Combined with the above findings, robust H_∞filtering analysis and synthesis issues of discrete time-varying delay systems are discussed in the next, using the method of reciprocal convex combination, combined with the nature of Jason integral inequality, results of the formal system H_∞capability and sufficient conditions for the existence of robust H_∞ filters and parameters are given in the form of LMI, respectively. MATLAB LMI toolbox is used to facilitate to solve. Verifying by numerical examples shows the correctness and validity of the proposed filter design methods.To apply the result of the robust filter design to the actual system, mathematical modeling of two-wheeled self-balancing robot and robust H_∞filter design problem are also studied in this distertation. Specifically, self-balancing the car’s body structure and model of Newtonian mechanics modeling and kinematics analysis are researched, and for speed control subsystem corresponding discrete robust H_∞filter is designed. The experimental verification of the effectiveness of the filter is given.