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This article presents a new dynamic triggering mechanism for fault‐tolerant control of linear systems. In this mechanism, the dynamic threshold is constructed by instantaneous and averaged triggering errors with its bounds. Consequently, it can be automatically adjusted between the bounds. A new intermediate observer is built in the proportional‐integral form to improve the estimation accuracy. The corresponding fault‐tolerant controller is explored to actively compensate unknown faults. By resorting to the Lyapunov stability theory, a sufficient condition is obtained in terms of linear matrix inequalities to make the closed‐loop system uniformly ultimately bounded with the required H∞$$ {H}_{\infty } $$ performance. The elitist nondominated sorting genetic algorithm version II (NSGA‐II) is adopted to realize the multiobjective optimization of the H∞$$ {H}_{\infty } $$ performance index γ$$ \gamma $$ and the allowable inter‐event time Tk$$ {T}_k $$. Finally, the proposed scheme is verified with two simulation examples. [ABSTRACT FROM AUTHOR]