Containment control of fractional-order multi-agent systems with time-varying delays |
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Authors: | Huiyang Liu Guangming Xie Yanping Gao |
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Institution: | 1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;2. Intelligent Control Laboratory, College of Engineering, Peking University, Beijing 100871, China;3. College of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China |
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Abstract: | In this paper, containment control problems of networked fractional-order multi-agent systems with time-varying delays are studied. The normalized directed graphs are employed to characterize the communication topologies. Two sampled-data based containment control protocols are proposed, which can overcome the time-varying delays and switching topologies. It is interestingly found that the decays of the closed-loop systems correspond to the Mittag-Leffler function and its approximation, which are the extensions of the exponential function and its approximation, respectively. Based on the algebraic graph theory, the properties of row-stochastic matrix, and the relation between the topologies and the matrices, some conditions for containment control are established. For the fixed topology, a necessary and sufficient condition is obtained; and for the switching topology, a sufficient condition is provided. Finally, the theoretical results are illustrated by several numerical simulations. |
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Keywords: | Corresponding author |
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