Dissipativity theory and applications of nonlinear stochastic systems with Markov jump and Levy noise

Authors：Li, Mengling; Ouyang, Zhengyong; Deng, Feiqi^*; Wu, Ze-Hao

Source：Communications in Nonlinear Science and Numerical Simulation, 2021, 99: 105796.

DOI：10.1016/j.cnsns.2021.105796

• Stochastic dissipativity
• Markov jump
• Levy noise
• LaSalle-type stability
• Stochastic KYP conditions
• Stochastic feedback passivity

This paper focuses on the stochastic dissipativity theory and applications for nonlinear stochastic systems with Markov jump and Levy noise. First, based on the dissipation inequality, multi supply rates, multi storage functions and stochastic analysis tools, the stochastic dissipation theory is established. And then the results can be utilized to obtain the sufficient conditions for LaSalle-type stability theorem of stochastically dissipative system. In addition, the conclusions on extended stochastic Kalman-Yakubovich-Popov (KYP) conditions and stochastic feedback passivity are also derived. Finally, two examples are given to validate the effectiveness of our results.

• Institution
  佛山科学技术学院