Model reduction of constrained mechanical systems in M-M.E.S.S. ⁎ ⁎The second author is supported by the German Research Foundation (DFG) within the priority program 1897: 'Calm, Smooth, Smart – Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation'

We discuss balanced truncation model reduction of constrained mechanical systems. The incorporation of the algebraic constraints leads to linear differential-algebraic control systems of index 2 or 3. Then for the square-root method in balanced truncation, the solution of projected Lyapunov equations is required. In this paper we discuss how to avoid the explicit construction of the projectors and the formulation of a projection-avoiding balanced truncation method which is suitable for efficient numerical computations. We have implemented this method in the Matlab package M-M.E.S.S. and present some numerical results for illustration.