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...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI
2022
|
Subjects: | |
Online Access: | View Fulltext in Publisher |
LEADER | 01514nam a2200181Ia 4500 | ||
---|---|---|---|
001 | 10.3390-math10132221 | ||
008 | 220718s2022 CNT 000 0 und d | ||
020 | |a 22277390 (ISSN) | ||
245 | 1 | 0 | |a On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations |
260 | 0 | |b MDPI |c 2022 | |
856 | |z View Fulltext in Publisher |u https://doi.org/10.3390/math10132221 | ||
520 | 3 | |a 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. © 2022 by the authors. Licensee MDPI, Basel, Switzerland. | |
650 | 0 | 4 | |a discontinuous differential equations |
650 | 0 | 4 | |a finite/fixed-time stability |
650 | 0 | 4 | |a lyapunov stability |
700 | 1 | |a Li, L. |e author | |
700 | 1 | |a Wang, D. |e author | |
773 | |t Mathematics |