Reachable set estimation and H_∞$H_\infty$ performance for delayed fuzzy multi-agent systems under false data injection attacks

Addressed in this paper is the reachable set estimation (RSE) problem for fuzzy-model-based leader-follower multi-agent systems with time-varying delays and false data injection attacks. First, the aperiodic sampled-data control is designed for the follower agents with randomly occurring false data injection attacks. Then, using the Kronecker product, the error system between the leader and the follower is obtained in a compact general form. Next, a novel Lyapunov-Krasovskii functional is constructed with the knowledge of sampling patterns and time-varying delays. In the framework of linear matrix inequalities, sufficient consensus conditions are determined from the (Formula presented.) performance index and Lyapunov theory to guarantee that its reachable set is enclosed by an ellipsoid in the existence of bounded perturbations. In the end, the Duffing Van der Pol oscillator and the single-link robot arm models are employed to validate the derived theoretical results.