Stability conditions for n-d control systems on the basis of the doubly similarity transformation and Lagrange solutions

The aim of this work is investigate the stability conditions for multi dimensional discrete linear control system given by the state space description model. The partial difference equations defining the state space model has two transition matrices: one related to the current states and the other one corresponding to previous states. Similarly, the feedback law constituted by the matrices of the current and previous states. To achieve it, the feedback control system is doubly transformed by means of similarity transformations; and their solutions are pursued on the basis of the Lagrange method.