Observer design for 2D discrete systems with delays

This paper is concerned with the design of an observer controller for 2D discrete system with delays, whose counterpart without delay terms is the 2D discrete Roesser state space model. The design objectives are the asymptotic stability and disturbance attenuation requirements. The key point is that the Lyapunov function presented here allows us to solve the problem in the linear matrix inequalities (LMIs) formalism, which is used to establish the controller for both the memoryless and memory state feedback control laws. Two numerical examples are presented to show how these LMIs are handled to determine the controller. Finally, it is interesting to note that the design of an observer on the basis of LMIs for 2D systems with delays has not been solved yet.