Stabilization of Discrete 2 D Switching Systems

Introduction

In many modeling problems of physical processes, a 2D switching representation is needed. One can cite 2D physically based model for advanced power bipolar devices [107] and heat flux switching and modulating in thermal transistor [124]. This class of systems can correspond to 2D state pace or 2D time space switching systems.

In the last two decades, the two-dimensional (2D) system theory has been paid considerable attention by many researchers. The 2D linear models were introduced in the seventies [87, 88, 93] and have found many applications, such as in digital data filtering, image processing [141], modeling of partial differential equations [127], etc. It is well known that 2D systems can be represented by different models as Roesser model, Fornasini-Marchesini model and Attasi model. For a complete description of these models and methods to transform the system from a model type to another, one can consult [109].