Optimal control for 2-D systems under malicious attacks

This paper investigates the H-infinity control problem for the cyber-physical systems (CPSs) described by two-dimensional (2-D) Roesser model subject to denial-of-service (DoS) attacks. First of all, the DoS attacks are characterized by the concepts of DoS frequency and DoS duration. Then, according to the intermittent characteristic of DoS attacks, the original 2-D CPSs are rewritten as a class of switched systems. Further, by means of Lyapunov theory for switched systems, the exponential stability and H-infinity noise attenuation performance for the resultant 2-D closed-loop dynamic are discussed. Sufficient conditions for the existence of desired H-infinity controller are established in terms of linear matrix inequalities (LMIs), and then the design scheme of the corresponding controller is transformed into a convex optimization problem. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method.