Stability Analysis of Input-Output Linearization Control With LuGre Friction Model Using Lyapunov Exponents

This work performs stability analysis on a control system partially modeled by LuGre friction model. Such a friction model has been proved sufficient to account for many features of friction. However, two parameters in the friction model, σ₀ and σ₁, are extremely difficult to be identified in real-world applications and the parameter errors (disturbances) coming from the measurements are therefore expected. In this work, we present a systematic methodology to rigorously analyze the effect of the disturbances mentioned above on the control system stability. The obtained analysis result clearly shows the robustness of the selected control law (input-output linearization control law). Lyapunov exponents calculated for two disturbed systems and our stability analysis result are in good agreement. The proposed methodology can be applied to other control laws of interest to examine their robustness.