Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks
This paper is concerned with the controllability problem of impulsive singularly perturbed systems (ISPSs). A new analytical approach is developed by integrating the merits of the fast–slow decomposition, Chang transformation and Gram-like matrix, and then some ε-independent necessary and sufficient...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/151324 |
| _version_ | 1811685540921081856 |
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| author | Yang, Wu Wang, Yan-Wu Guan, Zhi-Hong Wen, Changyun |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Yang, Wu Wang, Yan-Wu Guan, Zhi-Hong Wen, Changyun |
| author_sort | Yang, Wu |
| collection | NTU |
| description | This paper is concerned with the controllability problem of impulsive singularly perturbed systems (ISPSs). A new analytical approach is developed by integrating the merits of the fast–slow decomposition, Chang transformation and Gram-like matrix, and then some ε-independent necessary and sufficient controllable conditions are obtained. In addition, the upper bound of ε is given when deriving the sufficient controllable conditions. Moreover, a new type of heterogeneous multiplex multi-time-scale networks is introduced and can be further modeled by ISPSs. Based on matrix theory and graph theory, some intuitive and easy-to-test criteria are deduced for the controllability of the proposed networks. It is shown that the network topology, the nodal dynamics, the leader selection, and the inner-coupling interconnection are important controllable factors. Several numerical examples are presented to show the effectiveness of the proposed results. |
| first_indexed | 2024-10-01T04:46:09Z |
| format | Journal Article |
| id | ntu-10356/151324 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:46:09Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1513242021-06-22T04:40:30Z Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks Yang, Wu Wang, Yan-Wu Guan, Zhi-Hong Wen, Changyun School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Controllability Singularly Perturbed Systems This paper is concerned with the controllability problem of impulsive singularly perturbed systems (ISPSs). A new analytical approach is developed by integrating the merits of the fast–slow decomposition, Chang transformation and Gram-like matrix, and then some ε-independent necessary and sufficient controllable conditions are obtained. In addition, the upper bound of ε is given when deriving the sufficient controllable conditions. Moreover, a new type of heterogeneous multiplex multi-time-scale networks is introduced and can be further modeled by ISPSs. Based on matrix theory and graph theory, some intuitive and easy-to-test criteria are deduced for the controllability of the proposed networks. It is shown that the network topology, the nodal dynamics, the leader selection, and the inner-coupling interconnection are important controllable factors. Several numerical examples are presented to show the effectiveness of the proposed results. 2021-06-22T04:40:30Z 2021-06-22T04:40:30Z 2019 Journal Article Yang, W., Wang, Y., Guan, Z. & Wen, C. (2019). Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks. Nonlinear Analysis: Hybrid Systems, 31, 123-134. https://dx.doi.org/10.1016/j.nahs.2018.08.011 1751-570X 0000-0002-4722-1332 https://hdl.handle.net/10356/151324 10.1016/j.nahs.2018.08.011 2-s2.0-85052928035 31 123 134 en Nonlinear Analysis: Hybrid Systems © 2018 Elsevier Ltd. All rights reserved. |
| spellingShingle | Engineering::Electrical and electronic engineering Controllability Singularly Perturbed Systems Yang, Wu Wang, Yan-Wu Guan, Zhi-Hong Wen, Changyun Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks |
| title | Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks |
| title_full | Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks |
| title_fullStr | Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks |
| title_full_unstemmed | Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks |
| title_short | Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks |
| title_sort | controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks |
| topic | Engineering::Electrical and electronic engineering Controllability Singularly Perturbed Systems |
| url | https://hdl.handle.net/10356/151324 |
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