An Observer Controller Design Method for 2-D Discrete Control Systems

This work is concerned with the design of observer controllers for 2-d (2-dimensional) discrete control systems. The 2-d systems considered here correspond to those ones called time-delayed systems in the ordinary 1-d control system theory counterpart, so that the system of partial difference equations has two composing matrices on the right hand side of the equality expressing the matrix equation. The controller is established in two steps; namely, part of the controller is designed so that one of the composing matrices is turned into a diagonal matrix whereas another part is defined by requiring the other composing matrix to have a Jordan canonical form. Stability of the compound control system consisting of the original 2-d system and the observer controller is guaranteed on the grounds of the Lagrange solution method for solving partial difference equations. Finally, the whole procedure is gathered in a design algorithm, and the computational procedure is depicted with a numerical example.