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

This paper focuses on the stochastic dissipativity theory and applications for nonlinear stochastic systems with Markov jump and Lévy 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.