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On the finite time stability for stochastic distributed parameter systems with free boundary-application to the micro-tunneling machine

We consider a finite-time stochastic stability for distributed parameter systems with free boundary condition. This mathematical model is deduced from the analysis of the tracking error of the installed pipe from the designed path in the micro-tunneling machine. After showing that the proposed mathematical system has a solution in some function spaces, we study the finite-time stability problem. The buckling phenomena of the installed pipe is simulated related to the derived sufficient conditions for the finite-time stability.