AIMS Mathematics, 2020, 5(4): 3682-3701. doi: 10.3934/math.2020238

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Constraint impulsive consensus of nonlinear multi-agent systems with impulsive time windows

1 Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, PR China
2 School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, and Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China

In this paper, the constraint impulsive consensus problem of nonlinear multi-agent systems in directed network is discussed. Impulsive time windows are designed for solving consensus problem of multi-agent systems. Different from the traditional impulsive protocol with fixed impulsive intervals, the impulsive protocol with impulsive time windows, where the impulsive instants can be changed randomly, is more effective and flexible. In addition, saturation impulse is also considered to restrict the jumping value of impulse beyond the threshold. Based on algebraic graph theory, matrix theory, and convex combination analysis, some novel conditions of impulsive consensus have been proposed. Our main results indicate that constraint impulsive consensus of the multi-agent systems via impulsive time windows can be achieved if the nonlinear systems satisfy suitable conditions. Numerical simulations are presented to validate the effectiveness of theoretical results.
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