Stabilization of discrete 2D behaviors by regular partial interconnection
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In this work, we consider linear, shift-invariant and complete two-dimensional (2D) discrete systems from a behavioral point of view. In particular, we examine behaviors with two types of variables: the variables that we are interested to control (the to-be-controlled variables) and the variables on which we are allowed to enforce restrictions (the control variables). The main purpose of this contribution is to derive necessary and sufficient conditions for the stabilization of the to-be-controlled variables by ‘attaching’ a controller to the control variables. This problem turns out to be related to the decomposition of a given behavior into the sum of two sub-behaviors. Moreover, we show that under certain conditions, it is possible to obtain a constructive solution and characterize the structure of the to-be-controlled behavior.
KeywordsTwo-dimensional behaviors Partial regular interconnection Stabilization Finite-dimensional autonomous behaviors
Mathematics Subject Classification (2000)93B05 93B07 93B25 93C05 93C35 93C65 93D15
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