Stability of two-step repetitive processes based on a matrix formulation

The stability of two-step repetitive processes will be considered. We assume signals depending on two spatial variables and the pass-number. In all cases of interest the pass lengths will be finite. Since all known approaches to the stability problem do not take this fact into account, the resulting statements concerning stability are of little help. To overcome this dilemma the process is reformulated into a vector-difference-equation of order 2 with the dimension LM as the product of the pass lengths. The stability of systems described by such equations has been investigated earlier. These results can be applied directly to the problem. Simple inequalities for the Fourier-transforms of the mask-coefficients are obtained. In the case of 3 times 3 masks, explicit stability conditions in the form of expressions for the mask-elements can be derived.

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