Passivity-Based Asynchronous Control of 2-D Roesser Markovian Jump Systems and Stabilization Under DoS Attacks

The passivity-based asynchronous control is tackled for 2-D Roesser Markovian jump systems (MJSs) and stabilization is guaranteed when 2-D MJSs are susceptible to Denial-of-Service (DoS) attacks. A novel jump model is proposed in this article, where the switching law of subsystems is regulated by the sum of the horizontal and vertical coordinates' values. This differs from the conventional jump model, which presumes that the transition probabilities are identical in both directions. The proposed jump model can avoid the mode ambiguity problem. Given the openness and sharing nature of communication networks, they are susceptible to malicious cyber-attacks that impair system performance. The concept of global time is introduced to help characterize the jump law and construct DoS attack model. Besides, a hidden Markov model (HMM) is utilized to manage the inevitable mismatched mode problem induced by any delay or data dropouts. With the above considerations, several conditions are established for ensuring passivity performance of 2-D MJSs and stabilization when facing DoS attacks. Several equivalent solvable conditions are derived via decoupling strategy and matrix inequality technique. Finally, two simulation examples are provided to demonstrate the validity of the established theoretical results.