Design Of 2-D Robust H₂/H_∞ Filter Based On LMI Approach

With the development of modern industry, more and more 2-D discrete system model should be solved in practical project. The application of 2-D robust H₂ /H_∞filtering attract more attention in the international learning group, in terms of canceling the input noise, restoring the useful information of the system and reducing the sensitivity of the model the uncertainties effectively. In the view of solving the filtering problem for the observation system availably, the LMI has been greatly used in the filtering field in recent years. With the development of the LMI toolbox in Mat-lab, the method through which the 2-D robust H₂ /H_∞filtering can be achieved using LMI, has become a research hot spot in the filtering field.In recent years, there have been many results toward 2-D robust H₂ /H_∞filtering problem through the international field. But the inherent computational complexity of the Riccati method affects the application of the filtering greatly. So, the new algorithm method which reduces the computational amount is presented in this paper. As well as the LMI toolbox will make it more convenient. The new method 2-D robust H₂ /H_∞filtering design algorithm is based on LMI.The 2-D robust H₂ /H_∞filtering method via LMI is studied in detail on the basis of the 2-D robust H₂ /H_∞filtering algorithm in this paper. Some concepts and the settle thoughts are figured out. While the basic knowledge has been applied to the H∞control theory. Finally, the related theory of the 2-D robust H₂ /H_∞filter is gained.The main work in this paper is as followsFirstly, 1-D robust H₂ /H_∞filter design.First of all, the problem of H∞filter description and the corresponding value of the known system are provided, then its solutions of continuous system. Based on this, in the view of nominal system, H∞norm is cited in the filtering error dynamic equation, which makes the transform function of estimated disturbance error less thanγ. Thus, it is considered as the constraint condition and theorem of filter is derived. With unknown noise statistical characteristics and uncertain parameters, robust H∞filter theorem is given, thus it improves that of typical filter that requires known system model. Through LMI simulink tools in Matlab, LMI inquations in above theorems are determined whether there reasonable solutions. Furthermore, whether H∞and robust H∞filters exist are determined. If filters exist, coefficient matrices are solved to confirm the models for filters and it is very convenient for analyzing its performance. Additionally, robustness of robust H∞filter is analyzed when uncertainty involves.Secondly, 2-D robust H₂ /H_∞filter design.Theorems for 2-D H∞, 2-D H 2 2-D robust H∞and 2-D robust H 2 filters are proved and simulations are conducted to verify their feasibilities. In order to explain characteristics and signs in the proof clearly, basic knowledge for 2-D linear system, 2-D bounded lemmas, 2-D filter model and norm of 2-D H∞and H∞are introduced. Based on this, basic knowledge in 2-D system space is applied into H∞control theory, and basic concept of 2-D H∞theory is given. Meanwhile, combined with LMI method, 2-D H∞, 2-D H 2 2-D robust H∞and 2-D robust H 2 filter algorithms are proposed.Finally, coefficient parameter matrices for 2-D filters are solved by LMI inequation through LMI simulink tools in Matlab. Hence, 2-D filters are designed completely. Filter performance is evaluated by the index of least square of errors. Through simulations, correction and effectiveness of 2-D filters and proposed LMI algorithm are verified.There is some significance for this paper, which are as followsFirstly, nowadays there are many reports for 2-D robust H₂ /H_∞filtering problems overseas, but in the domestic, it is very marginal. In this paper, in the view of multi-dimension, unknown uncertainty and noise statistical characteristics, basic knowledge in 2-D system space is applied into H∞control theory,afterwards, 2-D H∞, 2-D H 2 2-D robust H∞and 2-D robust H 2 filter existing theorems are demonstrated, also feasibility of LMI are proved. All these provide much more effective way to further study 2-D robust H₂ /H_∞filters.Secondly, a novel 2-D robust H∞algorithm based LMI is proposed. It reduces computation time on a certain extent; also it is very easy to realize the algorithm using LMI. Therefore a new solving method is built radically. As the more and more deep research on 2-D robust H₂ /H_∞filters, 2-D robust H₂ /H_∞filters based on LMI especially with less computation will be a key focus.