Robustness analysis of global exponential stability of nonlinear stochastic systems with respect to neutral terms and time-varying delays

• Published in: Advances in difference equations Vol. 2015; no. 1; pp. 1 - 14
• Main Authors: Xu, Zhiying, Liu, Wei, Li, Yan, Hu, Junhao
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 31.03.2015; Springer Nature B.V
• Subjects: Analysis; Criteria; Delay; Difference and Functional Equations; Functional Analysis; Inequalities; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinearity; Ordinary Differential Equations; Partial Differential Equations; Robustness; Stability; Stochastic systems; Time delay; robustness analysis; nonlinear stochastic systems; transcendental equation; mean square exponential stability
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-015-0364-3

In this paper, we consider a class of nonlinear stochastic systems with respect to neutral terms and time-varying delays. Given a globally exponentially stable nonlinear stochastic system, the robustness of the global exponential stability of the system subject to a time delay and a neutral term can be derived by a subtle inequality and a transcendental equation. The upper bound of the allowable time delays and the neutral terms contraction coefficient is easy to verify and implement. Finally, an example with a numerical simulation is given to illustrate the presented criteria.