Abstarct: In last two decades, the two-dimensional systems theory has been payed a considerable attention and developed by many researchers. These systems have found many applications such as in image processing, modeling of physical processing and dramating robots, etc. From time that these systems introduced, many scientists proposed different models that most popular are Roesser model (1975), Fornasini(1978), marchesini(1976) and curek(1996). Because of generalization of Roesser model regadr to other models, I choice this model in my thesis. In this thesis we consider two-dimensional linear discrete-time systems that introduced by Roesser model, study stability of these systems and camputing optimal time state feedback matrix. The method that we used in this thesis is making an increased matrix by supposed matrices, then with using priliminary row application and parallel calumn application, changingto the Echlon standard form then the vector companion form and finally with using of the vector companion form we obtain optimal time state feedback matrix for the twodimensiona system.