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Stabilization of discrete 2D behaviors by regular partial interconnection

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Abstract

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.

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Authors and Affiliations

  1. Department of Ingenieria de Sistemas y Automatica, Universidad de Valladolid, Valladolid, Spain

    Diego Napp

  2. Department of Electrical and Computer Engineering, Faculty of Engineering, University of Oporto, Oporto, Portugal

    Paula Rocha

Authors
  1. Diego Napp
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  2. Paula Rocha
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Correspondence to Diego Napp.

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Napp, D., Rocha, P. Stabilization of discrete 2D behaviors by regular partial interconnection. Math. Control Signals Syst. 22, 295–316 (2011). https://doi.org/10.1007/s00498-011-0060-0

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  • DOI: https://doi.org/10.1007/s00498-011-0060-0

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