Robust Control And Filtering For Uncertain Systems

Robust control and filtering for uncertain systems have been the focus of the research in control theory. During the last years, many investigators have researched the two problems and presented many significant results. However, there exist many important problems to be solved, such as the problems of resilient control for 2-D systems; filtering for interconnected systems, the problem of designing robust controllers and filters for singular systems and nonlinear systems. The research on these problems will expedite the development of control theory greatly. Therefore, this paper will propose some research results in this field. The main results can be expressed as follows:Firstly, the problem of resilient guaranteed cost control for 2-D systems is considered. Based on L-K functional approach, we propose the sufficient conditions and resilient controllers design approaches for 2-D systems.Secondly, the problem of robust decentralized control for a class of interval large-scale systems is considered. We analyze the effects on the performances by uncertainties existing in system matrices and interconnected matrices. The design approach of controllers is given in term of LMI. Thirdly, based on robust control idea, this paper investigates the problem of robust filtering for uncertain discrete time-delayed systems, singular systems and large-scale systems respectively. This approach only requires the noise inputs to be energy-bounded instead of Gauss white noises. The main results can be expressed by LMI after some matrix manipulations.Finally, the problem of exponential filters for nonlinear time-delayed systems is considered. The filters designed by using the given approach can guarantee the stead-state and transient performance. By choosing suitable attenuation index, the perfect performances of filters can be attained. Simulation demonstrates the effectiveness of the presented results.