Abstract
A methodology for controlling nonlinear mechanical systems expressed in non-singular parametric descriptor quasi-linear parameter varying form is developed. For mechanical systems, this form is naturally obtained through the Lagrangian formulation. Use of this form avoids the explicit inversion of the mass matrix, thus eliminating the additional resulting linear fractional parameter dependence complexity. Parametric Lyapunov functions are used for the design. Sufficient conditions for the stability and dynamic output feedback control with guaranteed induced ${\cal L}_2$-norms from the disturbance to the controlled output are given. The conditions for the reduction of the solvability conditions to finite-dimensional linear matrix inequalities are provided. The results are shown on a two-link flexible manipulator example.
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