| Summary: | In this paper, the observer-based $ H_{\infty } $ PID control problem is studied for linear discrete-time systems subject to hybrid cyber attacks. Two sets of Bernoulli distributed stochastic variables are utilized to characterize the random nature of the false data injection attack and the replay attack. A sector-like bounded condition is exploited to constrain the malicious signal in the false data injection attack which reflects the certain tolerable bound on the difference between the attack signal and the true signal. Sufficient conditions for the existence of the expected observer-based $ H_{\infty } $ PID controller are given to ensure the exponential mean-square stability and the $ H_{\infty } $ performance. Then, the controller parameters are calculated by solving a matrix inequality. Finally, a simulation example is employed to demonstrate the effectiveness of the proposed control algorithm.
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