The design problem of the state filter for the generalized stochastic 2-D Roesser models, which appears when both the state and measurement are simultaneously subjected to the interference from white noise, is discussed. The well-known Kalman filter design is extended to the generalized 2-D Roesser models. Based on the method of “scanning line by line”,the filtering problem of generalized 2-D Roesser models with mode-energy reconstruction is solved. The formula of the optimal filtering, which minimizes the variance of the estimation error of the state vectors, is derived. The validity of the designed filter is verified by the calculation steps and the examples are introduced.
In this paper, the properties and concepts of dual systems of the two-dimensional singular Roesser models （2-D SRM） are studied. Two different concepts of the dual systems are proposed for the 2-D SRM. One is derived from the duality defined for two-dimensional singular general models （2-D SGM）-called the S-dual systems; the other one is defined based on 2-D SRM in a traditional sense-called the T-dual systems. It is shown that if a 2-D SRM is jump-mode free or jump-mode reachable, then it can be equivalently transformed into a canonical form of a 2-D SRM, for which the T-duality and the S-duality are equivalent. This will be of some perspective applications in the robust control of 2-D SRM.
