H_∞ Filter Design For Networked Control Systems Via Delta Operator Approach

Networked Control Systems(NCS) is proposed by the development of electronic information and computer technology. The NCS can replace the traditional point-to-point transmission in control system. The NCS has plenty of nice characters such as resource sharing, ease of expansion, ease of maintain, low system cost, well flexibility and so on. Filtering for network-based system is an important content in the field of control and information. The H_∞ filtering has a good robustness and the H_∞ indicator is the ideal performance indicator when the power spectral density of external signal is with uncertainty. By using delta operator some control problems of continuous time and discrete time systems can be considered by unified approach. And the delta operator approach can avoid ill-conditioned problems caused by the conventional shift operator model based theory when fast sampling. So the H_∞ filtering of NCS described by the delta operator is extremely meaningful.In this paper, we give the detail review about the filtering problem of networked control systems in recent years. And we focus on the H_∞ filtering of NCS via the delta operator approach. Research on the NCS with time-varying delay and packet dropout will be discussed respectively using delta operator. The main result is as below:First, a state equation to describe the networked control system with time-varying delay via delta operator approach is established. We can get the filter and filtering error equation with H_∞ performance. According to the related knowledge of H_∞ control, we can obtain the condition for the stability of the filtering error system and complete the design of the filter. The parameters of the H_∞ filter are derived as well.Second, the H_∞ filter of NCS with packet dropout is designed. The system is constructed as an asynchronous dynamic system with long time delay. By discretizing the system with the delta operator approach we can obtain the filtering error system. The stability of the system is described by a series of linear matrix inequality(LMI). And we also get the filter parameters.At last, the H_∞ filtering for NCS methods in this paper are all proved through the numerical validation. The filter parameters are derived. And the validity and feasibility are all confirmed.