We study the problems of robust stabilization and optimization of the equilibrium states of nonlinear mechanical systems. Sufficient conditions for the stabilization of a linear system with measured output feedback are formulated by means of the full-order state observers. The solution of the general problem of robust stabilization and the estimates of the quadratic performance criterion are presented for a family of nonlinear systems on examples of a one-link pendulum on a moving platform in the upper equilibrium position and a pendulum with flywheel control. The application of the obtained results is reduced to the solution of systems of linear matrix inequalities.
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Translated from Neliniini Kolyvannya, Vol. 17, No. 4, pp. 462–475, October–December, 2014.
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Kupriyanchyk, L.V. Robust Stabilization of Nonlinear Mechanical Systems. J Math Sci 212, 397–411 (2016). https://doi.org/10.1007/s10958-015-2672-2
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DOI: https://doi.org/10.1007/s10958-015-2672-2