Observer-based H∞ consensus for linear multi-agent systems subject to measurement outliers

The consensus problem has a crucial role in theoretical and practical aspects of interconnected systems, for instance in smart computing field. This paper is concerned with the observer-based H∞ consensus problem for a class of linear multi-agent systems subject to measurement outliers. In the addressed observer-based H∞ consensus problem, measurement outliers can affect the estimation accuracy and thus affect the consensus performance. To assuage the impact of measurement outliers, a control protocol based on an observer containing a saturation function with variable saturation limits is proposed. The purpose of this paper is to find a solution to the addressed H∞ consensus problem for a class of linear multi-agent systems subject to measurement outliers by designing an observer-based control protocol such that multi-agent systems can fulfill the H∞ consensus performance over a finite horizon. With the aid of Lyapunov theory, the sufficient condition is established to guarantee that the consensus error dynamic system satisfies the H∞ consensus performance. Then, the linear matrix inequality (LMI) approach is used to obtain the desired parameters of the observer-based control protocol. Finally, the effectiveness of the proposed control protocol is verified in a simulation environment. Aim: The purpose of this study is to find a solution to the addressed H∞ consensus problem for a class of linear multi-agent systems subject to measurement outliers. Methods: By choosing a suitable Lyapunov function, the sufficient condition is obtained, which can guarantee the consensus error dynamic system satisfying the given H∞ consensus performance. The LMI approach is employed to design the desired controller. With Matlab LMI toolbox, a numerical example was conducted to demonstrate the effectiveness of the proposed observer-based control protocol in the simulation environment. Results: A satisfactory consensus performance can be guaranteed for multi-agent systems subject to measurement outliers under the proposed observer-based control protocol. The constructed saturation function with variable saturation limits can mitigate the effect of measurement outliers by dynamically regulating saturation limits. Compared with the traditional observer-based control protocol, in this paper, the proposed observer-based control protocol shows robustness against measurement outliers. Conclusion: A solution to the addressed multi-agent consensus problem subject to measurement outliers was found by designing an observer-based consensus controller. The obtained results can be extended to sensor networks, neural networks, and nonlinear multi-agent systems.