Robust Adaptive Sliding Mode Security Control of Markov Jump Cyber-Physical Systems With Stochastic Injection Attacks Through Event-Triggered-Based Observer Approach

This article addresses the challenge of state observer design for sliding mode security control in Markov jump cyber-physical systems subjected to stochastic injection attacks. To enhance network efficiency, a dynamic event-triggered algorithm is introduced in the communication channel. First, the design begins with a Luenberger state observer featuring an adaptive compensator. This configuration aims to effectively counteract malicious attacks. Second, an integral sliding hyperplane is formulated within the estimation space, which serves as the foundation for deriving the sliding mode dynamics, ensuring robustness against disturbances. Recognizing the diversity of transition rates (TRs), an elastic sliding mode controller is designed to accommodate three distinct types of TRs, which is also strategically designed to guarantee reachability and maintain sliding motion. Third, stochastic stability with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> attenuation level is conducted separately for each type of TR. Correspondingly, the development of an algorithm for determining threshold parameters in triggered conditions is presented. Simultaneously, a proof of the nonexistence of Zeno behavior is provided, ensuring the stability and efficiency of the proposed system. Finally, a simulation study using a practical model is included to empirically demonstrate the validity of the proposed method in a real-world context.