Research On Filtering For 2-D Systems In Roesser Model

State-vector of the systems usually can not be getted directly from the system`s state-space models.we need to rebuild the state-vector by input or output information,or estimate a linear combination of the state-vector.Because of the existence of process noise and measured noise,we need filtering during rebuild the state-vector.Filtering problem and output-feedback control problem are a couple of duality problems. So filtering problem is always closely relative to modern control theory.At the beginning of 1980s,American researcher Roesser propounded the 2-D Roesser model,which can be recognized as the origin of linear discrete-time state-space theory. With the development of science and technology, the application domain of 2-D systems becomes more and more wide. Great interests had been excited in 2-D filtering theory. The kalman filtering theory which been accompanied by state-space theory, always plays an important role in both control and filtering theory. Expanding the 1-D kalman to 2-D system is of great practical value. However we need more effective recursive algorithm because of increasing computation, also because the difficulty in building a appropriate recursive model and dimension of the state vector is too large, The work, that using kalman filter in 2-D systems, progressed at a slow pace. Through the scholars` efforts, many important results have been made available.But kalman fitler needs a accurately known model and the statistical characteristic of the noise should been known, this disadvantage restricts the kalman filter`s practical application in a certain extent.As a result of environmental influences, models not only have process noise and measured noise, but also have a broad variety of uncertaintys itself. In order to suppress the noise, resume useful information, also reduce the system`s sensitivity to all kinds of uncertaintys, H∞control and filtering theory has been used in 2-D systems with parameter uncertaintys.In recent decades, Linear Matrix Inequality(LMI) method was widely used in robust control domain, Especially the advent of the LMI toolbox in Matlab software,made designing robust H∞filter via LMI approach more and more convenient. H∞theory need nerther an accurate model nor the statistical characteristic of the noise, so 2-D robust H∞filter design has been one of the research hot points in 2-D filtering domain. On a basis of 1-D kalman filtering and robust H∞filtering theory, this thesis focuses on 2-D Kalman fitlter technique and 2-D robust H∞filter technique.The thesis consists of four parts:(1).Filter design and controller design are a couple of duality problems,It needs many knowledge of system`s norm and state-space models.We first introduce the definition of the norm of singnal and system.2-D system is more complex than 1-D system,and it have many new properties,The 2-D Roesser models was given. Bounded real lemma and stability of systems are also introduced.All of these are basic theory of 2-D sysyems.The theorems of robust H∞filtering in this paper are described by LMI, We also introduce the knowledge of LMI.(2).2-D even n-D filteing theory are extened from 1-D filtering theory.They all have the same basic ideas. To make it easier to understand 2-D filteing theory, we introduce 1-D Kalman filter and robust H∞filter in detail. For particular numerical examples, we design kalman and robust H∞filter separately, simulation verifiy the filter`s performance.(3).We will be faced with difficulties in expanding 1-D kalman filter to 2-D systems.when the standed 1-D kalman filter is used in 2-D systems, the dimension of state-vector will increase,we call this phenomenon"dimension-disaster".This paper transforms the 2-D Roesser model to the regular 2-D FMII model by the method of variable substitution.We use a method called"scanning line by line"to get the 2-D kalman filter,which overcomes the"dimension-disaster".The"scanning line by line"approach is a direct expending from 1-D system to 2-D system,but the problems on stability of the filter remain open.(4).Polytopic-type uncertainty is a common form of the uncertainty.Based on the structured polynomially parameter-dependent method,in this paper,we obtain a less conservative filter for 2-D Roesser model.The main idea is based on homogeneous polynomially parameter-dependent matrices of arbitrary degree.With the increasing degree,more free variables are introduced to the LMI systems,the obtained H∞filter is less conservative.The numerical example shows the feasibility and advantage of the method. But, with the increasing degree, calculation also increase.Despite of that, the method is a good attemption in reduceing the filter`s conservation.There are some works need to be done in future:The methods designing 2-D filter which are used in this thesis need a great deal of calculation, we need to find new method with less calculation. Because of the essential differences between 1-D system and 2-D systems, Research on the theory of 2-D systems faces more difficulty. Speaking of the present development situation, 2-D theory remains a great deal problems, some even be the basic problems. Systems mentioned in this thesis are linear systems. Apparently practical systems are always nonlinear systems, there are a lot of works need to be done in 2-D nonlinear systems; In practical industrial operation and progress of physical, time-delay is common phenomenon.The problem of filter designing for 2-D systems with time-delay also need to be solved . In addition,2-D systems theory need more application research.