Stability and disturbance attenuation of 2-D discrete delayed systems via memory state feedback controller

Abstract

In this paper, we aim to investigate the two-dimensional (2-D) discrete control systems with delay terms in the dynamics and the outputs. And the results are established on the grounds of the linear matrix inequalities (LMIs) formulation. Basically, this work is concerned with: (1) developing a framework for testing the asymptotic stability of such systems; and (2) designing a state feedback control system to fulfill the disturbance attenuation objective. To accomplish it, an asymptotic stability condition, which is an extension of the one for the 2-D delayless discrete systems, is first pursued by means of the Lyapunov second method. Next, taken this into account, a condition for the existence of a memory controller that provides a feedback control system with the disturbance attenuation characteristic is established.