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Stability of a class of 2-d output feedback control systems

This paper is concerned with the asymptotic stability analysis of 2-dimensional (2-d) linear discrete systems with delay terms and such that the matrices of the dynamics (states) expressed in the state space representation can be transformed into diagonal matrices via the output feedback control. To accomplish it, we adopt the Lagrange method for solving the set of partial difference equations modeling the dynamics of the system, and analyse the conditions to guarantee the asymptotic stability. This approach allows us to establish explicit solutions to the system and understand the influence of the eigenvalues of the matrices on the stability of system. Finally, we stress that investigations of this kind is still a novelty to the best of author's knowledge.