Discrete state-space modeling for linearnth-order constant coefficient distributed-parameter systems

A systematic procedure is developed for state-space modeling and solving the dynamic behavior of any linearn order constant coefficient distributed-parameter system with two or more independent variables. The state-space model is a set of first-order linear difference equations and is also referred to as a discrete multidimensional state-space model. Transformation of a continuous distributed-parameter system into a discrete state-space model is based on the multidimensional Laplace-bilinear mapping technique. A procedure is outlined for converting the initial and boundary conditions of the system into a set of discrete conditions appropriate for the statespace model. Convergence of the state-space model's solution to the exact solution depends on the sampling rates of the independent variables and the ratio of increments. A few examples when state-space modeling of a distributed-parameter system is useful are: to estimate optimal feedback or optimal feedforward gains in active control applications; model reference optimal-distributed tracking systems; optimal tracking of desired trajectories; realtime system identification.