Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems
This paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using the max-separable ISS Lyapunov function method, a sufficient condition on ISS is given for general NIPS. On that basis, the ISS criteria for linear impulsive...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/14/1663 |
| _version_ | 1797526639322595328 |
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| author | Yiqing Xue Ping Zhao |
| author_facet | Yiqing Xue Ping Zhao |
| author_sort | Yiqing Xue |
| collection | DOAJ |
| description | This paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using the max-separable ISS Lyapunov function method, a sufficient condition on ISS is given for general NIPS. On that basis, the ISS criteria for linear impulsive positive systems (LIPS) and affine nonlinear impulsive positive systems (ANIPS) are given. Through them, ISS properties can be directly judged from the algebraic and differential characteristics of the systems. Then, utilizing the ISS criteria, state-feedback and impulsive controllers are designed for LIPS and ANIPS, respectively, which make the systems input-to-state stabilizable. Lastly, some numerical examples are given to verify the effectiveness of our results. |
| first_indexed | 2024-03-10T09:32:10Z |
| format | Article |
| id | doaj.art-2804dbdb4d8b4c78a29f148ca4307860 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:32:10Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2804dbdb4d8b4c78a29f148ca43078602023-11-22T04:20:20ZengMDPI AGMathematics2227-73902021-07-01914166310.3390/math9141663Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive SystemsYiqing Xue0Ping Zhao1School of Information Science and Engineering, Shandong Normal University, Jinan 250358, ChinaSchool of Information Science and Engineering, Shandong Normal University, Jinan 250358, ChinaThis paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using the max-separable ISS Lyapunov function method, a sufficient condition on ISS is given for general NIPS. On that basis, the ISS criteria for linear impulsive positive systems (LIPS) and affine nonlinear impulsive positive systems (ANIPS) are given. Through them, ISS properties can be directly judged from the algebraic and differential characteristics of the systems. Then, utilizing the ISS criteria, state-feedback and impulsive controllers are designed for LIPS and ANIPS, respectively, which make the systems input-to-state stabilizable. Lastly, some numerical examples are given to verify the effectiveness of our results.https://www.mdpi.com/2227-7390/9/14/1663nonlinear positive systemimpulsive systeminput-to-state stabilitymax-separable ISS Lyapunov function |
| spellingShingle | Yiqing Xue Ping Zhao Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems Mathematics nonlinear positive system impulsive system input-to-state stability max-separable ISS Lyapunov function |
| title | Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems |
| title_full | Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems |
| title_fullStr | Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems |
| title_full_unstemmed | Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems |
| title_short | Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems |
| title_sort | input to state stability and stabilization of nonlinear impulsive positive systems |
| topic | nonlinear positive system impulsive system input-to-state stability max-separable ISS Lyapunov function |
| url | https://www.mdpi.com/2227-7390/9/14/1663 |
| work_keys_str_mv | AT yiqingxue inputtostatestabilityandstabilizationofnonlinearimpulsivepositivesystems AT pingzhao inputtostatestabilityandstabilizationofnonlinearimpulsivepositivesystems |