Stability analysis of 2-d discrete delayed systems decoupled by means of feedback control

This paper is concerned with the asymptotic stability analysis of decoupled 2-dimensional (2-d) linear discrete delayed systems, in which the transition matrices are either completely or partially diagonalised by means of feedback control. To accomplish it, we adopt the Lagrange method approach for solving the set of partial difference equations modeling the dynamics of the decoupled systems, and analyze the conditions to guarantee the asymptotic stability. The key point is that we get explicit solutions to the equations as well as obtain some insights into the relationship between the structures of the matrices and the stability of the systems.