Design of the observer feedback gain for two-dimensional discrete systems

An algorithm for the state observer design of two-dimensional (2D) linear shift-invariant systems is proposed. For the case of one-dimensional (1D) systems, the necessary and sufficient conditions have been established for the problem, and an analytical solution for the observer feedback gain is given by K. Ogata (see "Discrete-Tone Control Systems", Prentice-Hall, 1995). Based on the well-known 1D results, a 2D observer feedback gain, K_e, is derived. Furthermore, an example is given to illustrate the feasibility of the present algorithm.