This paper considers the problem of positive real control for two-dimensional (2-D) discrete delayed systems in the Fornasini-Marchesini second local state-space model. Attention is focused on the design of dynamic output feedback controllers, which guarantee that the closed-loop system is asymptotically stable and the closed-loop transfer function is extended strictly positive real. We first present a sufficient condition for extended strictly positive realness of 2-D discrete delayed systems. Based on this, a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality (LMI). When the LMI is feasible, an explicit parametrization of a desired output feedback controller is presented. Finally, we provide a numerical example to demonstrate the application of the proposed method. © 2007 Elsevier B.V. All rights reserved.
Xu, H., Xu, S., & Lam, J. (2008). Positive real control for 2-D discrete delayed systems via output feedback controllers. Journal of Computational and Applied Mathematics, 216(1), 87–97. https://doi.org/10.1016/j.cam.2007.04.014