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Stability analysis of the linear discrete teleoperation systems with stochastic sampling and data dropout

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Document pages: 12 pages

Abstract: This paper addresses the stability conditions of the sampled-datateleoperation systems consisting continuous time master, slave, operator, andenvironment with discrete time controllers over general communication networks.The output signals of the slave and master robots are quantized with stochasticsampling periods which are modeled as being from a finite set. By applying aninput delay method, the probabilistic sampling system is converted into acontinuous-time system including stochastic parameters in the system matrices.The main contribution of this paper is the derivation of the less conservativestability conditions for linear discrete teleoperation systems taking intoaccount the challenges such as the stochastic sampling rate, constant timedelay and the possibility of data packet dropout. The numbers of dropouts aredriven by a finite state Markov chain. First, the problem of finding a lowerbound on the maximum sampling period that preserves the stability isformulated. This problem is constructed as a convex optimization program interms of linear matrix inequalities (LMI). Next, Lyapunov Krasovskii basedapproaches are applied to propose sufficient conditions for stochastic andexponential stability of closed-loop sampled-data bilateral teleoperationsystem. The proposed criterion notifies the effect of sampling time on thestability transparency trade-off and imposes bounds on the sampling time,control gains and the damping of robots. Neglecting this study undermines boththe stability and transparency of teleoperation systems. Numerical simulationresults are used to verify the proposed stability criteria and illustrate theeffectiveness of the sampling architecture.

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