An algorithm for model reduction of 2-D discrete time systems

In the context of model reduction of 2-D discrete time systems, several important properties of 2-D Gramians and balanced realizations are presented. Through a counterexample, the conjecture that the reduced model preserves stability is proven invalid. For separable systems, several interesting results regarding Gramians, norms, stability, and minimality are presented. For nonseparable systems, a simple, more efficient technique to compute Gramians is provided. The computation of Gramians in the separable case is possible through the solution of two pairs of discrete Lyapunov equations. An example is given to illustrate and justify the notions presented