On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations

Luke Li and Dongshu Wang
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Luke Li: School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
Dongshu Wang: School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Mathematics, 2022, vol. 10, issue 13, 1-14

Abstract: 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.

Keywords: finite/fixed-time stability; discontinuous differential equations; lyapunov stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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