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

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.