Double event-triggered leader-following consensus and fault detection for Lipschitz nonlinear multi-agent systems via periodic sampling strategy

This paper considers the problem of leader-following consensus and fault detection for a class of multi-agent systems with Lipschitz nonlinear dynamics. To reduce the amount of redundant information and avoid checking triggering conditions continually, this paper proposes an efficient network framework with a double periodic event-triggered mechanism. Based on the proposed framework, an improved fault detection observer and a consensus controller are designed. Then, the original problem is converted into a set of stability problems with constraints. According to Lyapunov–Krasovskii theorem and the free-weighting matrix technique, sufficient conditions for solving these stability problems are derived in the form of bilinear matrix inequalities (BMIs). Further, to eliminate the nonlinear terms of BMI and obtain optimal performance, two iterative algorithms based on linear matrix inequalities (LMIs) are developed. Two simulation examples are provided to verify the practicality and validity of the theoretical results.