Stability and Stabilization of a Flexible Manipulator

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Executive Summary

In this paper, the stability and stabilization of a neutral system with time-delay are treated. First, the flexible manipulator is modeled as a neutral time-delay system form. Then, based on the Lyapunov-Krasovskii functional theory, a delay dependant condition is proposed to test studied system stability, which is applied to a flexible manipulator model. The test shows that this flexible manipulator is instable and it should be stabilized. For this reason, other theorem is elaborated to determinate a feedback control based on Linear Matrix Inequalities (LMI). Finally, simulation results are presented to prove theorical development.

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