State Estimation And Robust Stabilization For Stochastic 2D Linear Discrete Systems

This dissertation concerns a series of problems such as the design of Kalman filters, measurement white noise estimators, set-membership estimators and robust stabilizers for stochastic 2-D linear discrete systems.First, we focus on the design of Kalman filters for stochastic 2-D FMII models. A generalized Kalman filter is proposed to stochastic 2-D FMII models that can minimize the variance of the estimation error of the state vectors. It is an extension of the well-known 1-D Kalman filter, which may avoid the dimension disaster in other relevant approaches.Then, the filtering problem of jump-mode reconstructable singular 2-D Roesser models is also solved via converting it into the filtering problem of regular 2-D FMII models by some appropriate vector transformations.Thirdly, based on the recursive 2-D Kalman filtering form proposed above, an optimal measurement white noise estimation methodology is presented for stochastic 2-D FMII models. It can handle the filtering, smoothing and prediction problems in a unified form. The statistical properties of singular stochastic 2-D discrete time systems are discussed.Fourthly, the problem of recursive estimation of state bounding of 2-D FMII models with noise in ellipsoidal sets is considered. A method based on optimal bounding ellipsoid (OBE) algorithmic procedure at each stage of updating is presented. The actual estimate is a set rather than a single vector in the state space. If necessary, the center of the ellipsoid can be regarded as the estimator of the state vector.Finally, the problem of robust stabilization for uncertain 2-D Markovian Jump systems in Roesser model with a class of generalized Lipschitz nonlinearities is discussed. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of the problem is given. A desired state feedback controller is constructed by solving certain LMIs.