Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems
This paper investigates the Lyapunov characterizations of input-to-output stability (IOS) and input-to-state stability (ISS) for nonlinear switched systems. The restriction on the negativity of derivatives of Lyapunov functions is relaxed; additionally, subsystems are not restricted to be ISS/IOS th...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Advanced Transportation |
| Online Access: | http://dx.doi.org/10.1155/2022/4436128 |
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| _version_ | 1832551248359849984 |
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| author | Shizhang Chen Chongyang Ning |
| author_facet | Shizhang Chen Chongyang Ning |
| author_sort | Shizhang Chen |
| collection | DOAJ |
| description | This paper investigates the Lyapunov characterizations of input-to-output stability (IOS) and input-to-state stability (ISS) for nonlinear switched systems. The restriction on the negativity of derivatives of Lyapunov functions is relaxed; additionally, subsystems are not restricted to be ISS/IOS throughout the state space. These problems are overcome by a newly proposed method, which extends multiple Lyapunov functions (MLFs) to an indefinite form. Indefinite multiple Lyapunov functions (iMLFs) are proposed on the basis of an inequality to estimate the upper boundary of the system state. Moreover, we apply the iMLFs method to verify the extended notions of IOS in a switched system. More relaxed sufficient conditions for ISS and IOS are proposed, a simulation experiment is carried out on a numerical example of the system, which demonstrates their effectiveness and superiority. |
| format | Article |
| id | doaj-art-4727d9c163a6424e898bd0eac00007c4 |
| institution | Kabale University |
| issn | 2042-3195 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Advanced Transportation |
| spelling | doaj-art-4727d9c163a6424e898bd0eac00007c42025-02-03T06:01:52ZengWileyJournal of Advanced Transportation2042-31952022-01-01202210.1155/2022/4436128Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched SystemsShizhang Chen0Chongyang Ning1School of Computer and Information EngineeringSchool of Computer and Information EngineeringThis paper investigates the Lyapunov characterizations of input-to-output stability (IOS) and input-to-state stability (ISS) for nonlinear switched systems. The restriction on the negativity of derivatives of Lyapunov functions is relaxed; additionally, subsystems are not restricted to be ISS/IOS throughout the state space. These problems are overcome by a newly proposed method, which extends multiple Lyapunov functions (MLFs) to an indefinite form. Indefinite multiple Lyapunov functions (iMLFs) are proposed on the basis of an inequality to estimate the upper boundary of the system state. Moreover, we apply the iMLFs method to verify the extended notions of IOS in a switched system. More relaxed sufficient conditions for ISS and IOS are proposed, a simulation experiment is carried out on a numerical example of the system, which demonstrates their effectiveness and superiority.http://dx.doi.org/10.1155/2022/4436128 |
| spellingShingle | Shizhang Chen Chongyang Ning Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems Journal of Advanced Transportation |
| title | Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems |
| title_full | Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems |
| title_fullStr | Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems |
| title_full_unstemmed | Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems |
| title_short | Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems |
| title_sort | improved multiple lyapunov functions of input to output stability and input to state stability for switched systems |
| url | http://dx.doi.org/10.1155/2022/4436128 |
| work_keys_str_mv | AT shizhangchen improvedmultiplelyapunovfunctionsofinputtooutputstabilityandinputtostatestabilityforswitchedsystems AT chongyangning improvedmultiplelyapunovfunctionsofinputtooutputstabilityandinputtostatestabilityforswitchedsystems |