Nonfragile Sliding Mode Control of Fractional‐Order Complex Networked Systems via Combination Event‐Triggered Approach

ABSTRACT This work addresses the problem of developing a nonfragile sliding mode observer for fractional‐order complex networked systems (FO‐CNS) under stochastic network attacks. The proposed approach employs a combination of event‐triggered techniques. First, a nonfragile fractional‐order state observer is developed, enabling the design of a suitable sliding surface function. Next, a combination event‐triggered condition (CETC) is introduced, utilizing sampled error and sliding mode error vectors. For guaranteeing the stability of closed‐loop systems, sufficient conditions are derived by solving the linear matrix inequalities. Moreover, an improved self‐triggered condition is developed to avoid Zeno behavior. This condition relies on a predefined event‐triggered mechanism. The Gronwall–Bellman inequality is employed to determine a positive lower bound of the trigger sequence, ensuring the avoidance of infinite triggering within a finite time interval. Finally, two numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed method.