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The stability and convergence of state, disturbance and parametric estimates of a robot have been analyzed using the Lyapunov method in the existing literature. In this paper, we analyze the problem of stochastic stability and also prove some results regarding behavior of statistically averaged Lyapunov energy function in the presence of jerk noise modeled as the sum of independent random variables hitting the robot at Poisson times. This type of noise is also called jerk noise in contrast to white Gaussian noise. Jerk noise is a Lévy process, i.e., a process with stationary independent increments, and is the natural non-Gaussian generalization of white Gaussian noise. Jerk noise can successfully be used to model hand tremor occurring at sporadic time intervals. We also study here the problem of time delay estimation in Lévy noise.

Classical robots perturbed by Lévy processes: analysis and Lévy disturbance rejection methods