Robust Secure Tracking Control for Uncertain 2-D Discrete Systems in a Networked Environment

This article investigates the robust secure output tracking control for a class of uncertain two-dimensional (2-D) networked control systems. The 2-D systems are described by the well-known Fornasini–Marchesini (FM) local state-space model, the parameter uncertainties are assumed to reside in a polytopic region, and the deception attacks are supposed to occur randomly in the transmission process. In the problem formulation, Bernoulli random variables are used to characterize the phenomena of deception attacks. As main results, a novel $H_{\infty }$ performance analysis condition for the augmented closed-loop system is proposed by using a novel parameter-dependent Lyapunov function and some zero equalities. Furthermore, both parameter-dependent and parameter-independent controllers have been designed, respectively, such that the output of the 2-D systems tracks the output of a given reference model well in the $H_{\infty }$ sense. The design conditions are presented in terms of linear matrix inequalities (LMIs). In the end, a numerical simulation on a practical thermal process is applied to illustrate the effectiveness of the proposed method.