Under an ISS Lyapunov condition and a mild assumption on disturbance probabilities, the state of a stochastic nonlinear system converges with probability 1 to the minimal robust positively invariant set.
Input-to-state stabi lity of robust receding horizon control with an expected value cost,
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Convergence of stochastic nonlinear systems and implications for Stochastic Model Predictive Control
Under an ISS Lyapunov condition and a mild assumption on disturbance probabilities, the state of a stochastic nonlinear system converges with probability 1 to the minimal robust positively invariant set.