Discrete-time feedback stabilization for neutral stochastic functional differential equations driven by G-Levy process

This paper mainly discusses the exponential stability of neutral stochastic functional differential equations with G-Levy jump. For a given mean square exponential unstable neutral stochastic differential equations with G-Levy jump, a discrete-time feedback control in the drift part is designed to realize feedback stability and the H-infinity stable cadlag solution of corresponding systems is obtained. The upper bound of state observation duration of the corresponding systems is derived by extending Mao's method. Further up, the exponential stabilization conditions are established and some exponential stabilities of the solutions are proved by using the G-Lyapunov functional method. Moreover, an example is presented to verify the obtained results.

Automated summary

This paper discusses the exponential stability of neutral stochastic functional differential equations with G-Levy jump. A discrete-time feedback control is designed to achieve feedback stability for a given mean square exponential unstable neutral stochastic differential equation. The H-infinity stable cadlag solution of the corresponding systems is obtained. The upper bound of state observation duration is derived and exponential stabilization conditions are established using the G-Lyapunov functional method. An example is presented to verify the results.