Iterative learning control for a two-dimensional discrete Fornasini–Marchesini system with deception attacks

This article addresses the security control issues for a two-dimensional (2D) discrete system in the second Fornasini–Marchesini's model (FMM) under deception attacks (DAs) using two kinds of iterative learning control (ILC) laws with the partial information and delay. ILC has been successfully applied to a one-dimensional (1D) system. Compared to the 1D system, the intricate characteristics of the 2D system render analysis and design significantly more challenging, especially when DAs are additionally involved. For convenience, the second FMM is transformed into a 1D model using the novel vector supplement and matrix construction algorithms first. To comprehensively investigate both secure and insecure issues, a 1D transformation system is constructed subject to DAs. Furthermore, two criteria are derived for insecurity and security under two proposed ILC laws. Finally, numerical results are presented to demonstrate the effectiveness of the proposed conditions.