On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations
We investigated the finite/fixed-time stability (FNTS/FXTS) of discontinuous differential equations (DDEs) in this paper. To cope with differential equations that were discontinuous on the right-hand side, we utilized the Filippov solution, which is widely used in engineering. Under the framework of...
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/13/2221 |
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| author | Luke Li Dongshu Wang |
| author_facet | Luke Li Dongshu Wang |
| author_sort | Luke Li |
| collection | DOAJ |
| description | We investigated the finite/fixed-time stability (FNTS/FXTS) of discontinuous differential equations (DDEs) in this paper. To cope with differential equations that were discontinuous on the right-hand side, we utilized the Filippov solution, which is widely used in engineering. Under the framework of the Filippov solution, we transformed this issue into an FNTS/FXTS problem in the corresponding functional differential inclusion. We proposed some new FNTS/FXTS criteria, which will have important applications in the field of control engineering. It is worth mentioning that the coefficient function in the inequality satisfied by the Lyapunov function (LF) could be indefinite. Moreover, our paper gave a new estimation for the settling time (ST). Finally, two illustrative examples were given to demonstrate the validity and feasibility of the proposed criteria. |
| first_indexed | 2024-03-09T04:02:23Z |
| format | Article |
| id | doaj.art-4ac96934a10e43889c5ffbe93d6994c4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:02:23Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4ac96934a10e43889c5ffbe93d6994c42023-12-03T14:11:51ZengMDPI AGMathematics2227-73902022-06-011013222110.3390/math10132221On Finite/Fixed-Time Stability Theorems of Discontinuous Differential EquationsLuke Li0Dongshu Wang1School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, ChinaSchool of Mathematical Sciences, Huaqiao University, Quanzhou 362021, ChinaWe investigated the finite/fixed-time stability (FNTS/FXTS) of discontinuous differential equations (DDEs) in this paper. To cope with differential equations that were discontinuous on the right-hand side, we utilized the Filippov solution, which is widely used in engineering. Under the framework of the Filippov solution, we transformed this issue into an FNTS/FXTS problem in the corresponding functional differential inclusion. We proposed some new FNTS/FXTS criteria, which will have important applications in the field of control engineering. It is worth mentioning that the coefficient function in the inequality satisfied by the Lyapunov function (LF) could be indefinite. Moreover, our paper gave a new estimation for the settling time (ST). Finally, two illustrative examples were given to demonstrate the validity and feasibility of the proposed criteria.https://www.mdpi.com/2227-7390/10/13/2221finite/fixed-time stabilitydiscontinuous differential equationslyapunov stability |
| spellingShingle | Luke Li Dongshu Wang On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations Mathematics finite/fixed-time stability discontinuous differential equations lyapunov stability |
| title | On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations |
| title_full | On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations |
| title_fullStr | On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations |
| title_full_unstemmed | On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations |
| title_short | On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations |
| title_sort | on finite fixed time stability theorems of discontinuous differential equations |
| topic | finite/fixed-time stability discontinuous differential equations lyapunov stability |
| url | https://www.mdpi.com/2227-7390/10/13/2221 |
| work_keys_str_mv | AT lukeli onfinitefixedtimestabilitytheoremsofdiscontinuousdifferentialequations AT dongshuwang onfinitefixedtimestabilitytheoremsofdiscontinuousdifferentialequations |