Stability of random impulsive coupled systems on networks with Markovian switching

Abstract

This article is intended to study global asymptotical stability in probability for random impulsive coupled systems on networks with Markovian switching. Two cases are considered. (1) Continuous dynamics are stable while impulses are unstable; (2) impulses are stable while continuous dynamics are unstable. To begin with, based on Lyapunov method as well as graph-theoretic technique, several new stability criteria in two cases are derived, that are, the Lyapunov-type criteria and the coefficients-type criteria. Then main results are used for a class of random impulsive coupled oscillators. Finally, the effectiveness of the obtained results is verified by numerical simulations.

Keywords:

• Random coupled systems
• impulsive effects
• global asymptotical stability in probability
• Markovian switching
• graph-theoretic technique

Additional information

Funding

This work was supported by Shandong Province Natural Science Foundation (Nos. ZR2018MA005, ZR2018MA020, ZR2017MA008); the Key Project of Science and Technology of Weihai (No. 2014DXGJMS08) and the Innovation Technology Funding Project in Harbin Institute of Technology (No. HIT.NSRIF.201703)