Secure Control of Markovian Jumping Systems Under Deception Attacks: An Attack-Probability-Dependent Adaptive Event-Triggered Mechanism

This article considers the secure control of Markovian jumping systems (MJSs) under stochastic deception attacks that occurred in the communication network. Therein, the stochastic deception attack is described by a Bernoulli random variable. Considering the limited network bandwidth and the impact of deception attacks simultaneously, we propose an attack-probability-dependent adaptive event-triggered mechanism. Not only can it reduce the number of controller updates, but it can also adapt to the variation of system dynamics subject to deception attacks. A mathematical model is established for the closed-loop system under stochastic deception attacks. Then, a time-dependent looped functional is constructed to reduce the conservatism of stability results. The norm of the system state is estimated, and based on the discrete-time Lyapunov theory, a less conservative stability criterion is derived. Then, an easy-to-implement design algorithm for the controller gain is given so that the exponential stabilization in the mean square sense can be realized for the MJS subject to stochastic deception attacks. Finally, an electrical circuit example is provided to validate the feasibility and superiority of the presented method.