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Input-to-state Stability of Impulsive Stochastic Nonlinear Systems Driven by G-Brownian Motion

Lijun Pan* and Jinde Cao*
International Journal of Control, Automation, and Systems, vol. 19, no. 2, pp.666-675, 2021

Abstract : This paper studies the input-to-state stability (ISS), stochastic input-to-state stability (SISS) and eλt-weighted input-to-state stability (eλt-ISS) of impulsive stochastic nonlinear systems driven by G-Brownian motion (IGSNSs). If the continuous stochastic systems are not ISS, the impulsive effects can stabilize the system for the fixed dwell-time sequences. However, if the continuous stochastic systems are ISS, the hybrid system can achieve ISS for destabilizing impulses with upper bound of the fixed dwell-time. Moreover, the average dwell-time condition is generalized to guarantee the ISS for IGSNSs based on G-Lyapunov method. Finally, an example is provided to illustrate the effectiveness of theoretical results.

Keyword : G-Brownian motion, impulse, input-to-state stability, stochastic systems.

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