Fault‐tolerant H∞$$ {H}_{\infty } $$ control for a fuzzy Markov jump systems with random actuator failure subject to attacks via AETM and its applications

Abstract Fault‐tolerant control for a class of fuzzy Markov jump systems with random actuator failures subject to deception attacks using adaptive event‐triggered mechanism is addressed in this study. The considered system is affected by external disturbances, network‐induced time delays, time‐varying delays, random actuator failures, and deception attacks simultaneously. Misleading data packets can be inserted into communication channels during deception attacks, affecting transmittal signal changes. Compared with the existing event‐triggered control methods, we propose an mode‐dependent adaptive event‐triggered mechanism (AETM) for fuzzy Markov jump systems to function between the sensor and controller, in order to reduce the amount of signal transmission. In addition, the offered adaptive law yields an event‐triggered threshold, enabling the control system to adaptively maintain satisfactory system performance. To model the occurrence of deception attacks and random actuator failures on the transmitted data, two different Bernoulli random variables are employed. The Lyapunov stability analysis indicates that the proposed AETM can ensure stabilization of the fuzzy Markov jump system in the presence of deception attacks and random actuator failures. Moreover, the controller gains and event‐triggered parameters are derived using the linear matrix inequality technique. Finally, illustrative examples, including a tunnel diode circuit system, are used to prove the correctness of the suggested control technique.