Delay-dependent stability of highly nonlinear neutral stochastic systems with non-differentiable delay

Mingxuan Shen; Huayu Wang; Chunhui Mei; Mingxuan Shen; Huayu Wang; Chunhui Mei

doi:10.3934/era.2026089

Electronic Research Archive

2026, Volume 34, Issue 3: 1988-2008. doi: 10.3934/era.2026089

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Research article

Delay-dependent stability of highly nonlinear neutral stochastic systems with non-differentiable delay

1.
Key Laboratory of Electric Drive and Control of Anhui Province, Anhui Polytechnic University, Wuhu 24100, China
2.
School of Mathematics-Physics and Finance, Anhui Polytechnic University, Wuhu 24100, China

Received: 07 January 2026 Revised: 05 February 2026 Accepted: 18 February 2026 Published: 05 March 2026

The aim of this paper is to investigate the delay-dependent stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs). Departing from most existing studies, the system under consideration incorporates a time-varying delay that is not required to be differentiable. A novel decomposition scheme for the drift coefficient is introduced, relaxing the conventional restrictive Lipschitz condition on the delay component. By constructing appropriate Lyapunov functionals and employing an M-matrix approach, delay-dependent conditions are derived to ensure moment stability for the considered highly nonlinear NSDDEs. Finally, an example is given to demonstrate the effectiveness of our new theory.
- neutral stochastic differential equations,
- M-matrix,
- delay-dependent stability,
- non-differentiable delay,
- Lyapunov functional
Citation: Mingxuan Shen, Huayu Wang, Chunhui Mei. Delay-dependent stability of highly nonlinear neutral stochastic systems with non-differentiable delay[J]. Electronic Research Archive, 2026, 34(3): 1988-2008. doi: 10.3934/era.2026089

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Abstract

The aim of this paper is to investigate the delay-dependent stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs). Departing from most existing studies, the system under consideration incorporates a time-varying delay that is not required to be differentiable. A novel decomposition scheme for the drift coefficient is introduced, relaxing the conventional restrictive Lipschitz condition on the delay component. By constructing appropriate Lyapunov functionals and employing an M-matrix approach, delay-dependent conditions are derived to ensure moment stability for the considered highly nonlinear NSDDEs. Finally, an example is given to demonstrate the effectiveness of our new theory.

References

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