pth moment asymptotic stability of stochastic delayed hybrid systems with Lévy noise

Abstract

The problem of pth moment asymptotic stability analysis is considered for stochastic delayed hybrid systems with Lévy noise. By virtue of Itô’s formula and M-matrix theories, we propose some sufficient conditions to guarantee the asymptotic stability and exponential stability of the system. The criterion of mean square asymptotic stability is derived as well for delayed neural networks with Lévy noise. A numerical example is provided to show the usefulness of the proposed asymptotic stability criterion.

Keywords:

• asymptotic stability
• stochastic hybrid systems
• Lévy noise
• generalised Itô’s formula
• M-matrix
• neural networks

Additional information

Funding

This work was partially supported by the Innovation Program of Shanghai Municipal Education Commission [Grant No. 13zz050]; the Natural Science Foundation of Shanghai [Grant No. 15ZR1401800], [Grant No. 12ZR1440200]; the Specialized Research Fund for the Doctoral Program of Higher Education [Grant No. 20120075120009].