Abstract
This paper addresses the asymptotic stability of multidimensional systems represented by first hyperquadrant causal linear difference equations whose coefficients are shift-varying. The results extend previous 1-D results, and include the derivation of a fixed region of stability in the parameter space, as well as a sequence of shift-variant parameter regions. In the case of a fixed parameter region, the largest stable hyperdiamond centered at the origin will be obtained. For the shift-variant case, it will be shown that the instantaneous stable parameter region always includes this hyperdiamond.
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Yost, S.A., Bauer, P.H. Robust stability of multidimensional difference equations with shift-variant coefficients. Multidim Syst Sign Process 5, 455–462 (1994). https://doi.org/10.1007/BF00989283
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DOI: https://doi.org/10.1007/BF00989283