Abstract
In this paper, we discussthe jump behavior and stability problems for 2-D linear shift-invariantsingular systems under the standard boundary conditions. It isshown that once a boundary condition or the input is inadmissiblein the classical sense, a group of non-causal or backward jumpsof the system states will be incited. This interpretation releasesthe conventional admissibility constraints on the boundary conditionsand inputs. Based on this observation, a systematic stabilitytheory is developed for 2-D singular systems. The well-knownbasic stability theorem for the 1-D singular systems or 2-D regularsystems is thus extended to the 2-D singular case.
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Zou, Y., Campbell, S.L. The Jump Behavior and Stability Analysis for 2-D Singular Systems. Multidimensional Systems and Signal Processing 11, 339–358 (2000). https://doi.org/10.1023/A:1008429611994
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DOI: https://doi.org/10.1023/A:1008429611994