LAUSR

In this paper, we propose a distributed state-and-fault estimation scheme for multiagent systems. The estimator is based on an $\ell _1$-norm optimization problem, which is inspired by sparse signal recovery in the field of compressive sampling. Two theoretical results are given to analyze the correctness of our approach. First, we provide a necessary and sufficient condition such that the state and fault signals are correctly estimated. The result presents a fundamental limitation of the algorithm, which shows how many faulty nodes are allowed to ensure correct estimation. Second, we analyze how the estimation error grows over time by showing that the upper bound of the estimation error depends on the previous state estimate and the number of faulty nodes. An illustrative example is given to validate the effectiveness of the proposed approach.