Stability analysis of constrained MPC with CLF applied to discrete-time nonlinear system |
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Authors: | XiaoGang Ruan XuYang Hou HangYing Ma |
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Affiliation: | 1. Institute of Information and System Sciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China 3. Ministry of Education key Lab for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an, 710049, China 2. College of Computer Science, Qinghai Normal University, Xining, 810003, China
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Abstract: | The problem of counting the number of spanning trees is an old topic in graph theory with important applications to reliable network design. Usually, it is desirable to put forward a formula of the number of spanning trees for various graphs, which is not only interesting in its own right but also in practice. Since some large graphs can be composed of some existing smaller graphs by using the product of graphs, the number of spanning trees of such large graph is also closely related to that of the corresponding smaller ones. In this article, we establish a formula for the number of spanning trees in the lexicographic product of two graphs, in which one graph is an arbitrary graph G and the other is a complete multipartite graph. The results extend some of the previous work, which is closely related to the number of vertices and Lapalacian eigenvalues of smaller graphs only. |
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Keywords: | constrained MPC stability analysis discrete-time system control Lyapunov function region of attraction |
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