Modeling of variable coefficient Roesser model for systems described by second-order partial differential equation

This paper addresses how a variable coefficient, two-dimensional (2D) multiple-input, multiple-output system described by second-order partial differential equations (PDEs) can be converted to a discrete variable coefficient Roesser model (RM). The following important question for its practical application is addressed: How does the choice of the finite difference operators for each differential operator and the respective integral intervals determine whether it is possible to arrive at a formulation according to the RM? This problem has not yet been addressed in generality. The results presented give a clear procedure to follow in the application of a finite difference discretization. The proposed prescription covers some important aspects, such as the state-space structure of variable coefficient difference equations, setting the states of the RM, and modeling of the RM, all of which are clearly interdependent. The proposed state-space modeling of a 2D system described by a PDE provides a powerful tool for analysis, design, and processing of variables and processes depending on two independent variables, one of which may be time. In particular, the model is very useful for 2D system control, such as observer design, optimal filter design, and state-feedback control methodologies presented in the literature.