A new method for the stability of discrete-time two-dimensional systems defined by the Roesser model

In this paper، We introduce a new method for the stability of discrete-time two-dimensional systems defined by the Roesser model، at first we introduce discrete-time two-dimensional linear systems described by Rosser model. Then، with using of this property that stability of discrete-time two-dimensional linear systems has a similar manner with stability of discrete time linear systems، we study stability of Rosser discrete-time two-dimensional systems. As for the stability of discrete time systems it is necessary to place all of its eigenvalues in unit circle. We use the partial eigenvalues assignment method for replace the desired eigenvalues instead eigenvalues of the open loop system which are outside the unit circle. For solving this problem، with using of partial Schur decomposition method، we decompose big matrix A to smaller matrices. Then with applying similarity transitions method for linear control systems، we allocate the desired spectrum to the system، so system will be stable. Finally، an illustrative example is presented.