Stability robustness of linear feedback-controlled mechanical systems in the presence of a class of unmodelled flexibilities

The author considers a class of linear mechanical systems containing flexible elements and subject to linear, memoryless, output-feedback controllers. The damping and stiffness properties of some of the flexible elements are parameterized linearly in μ^-1 and μ^-2, respectively, where μ>0 and these components become more rigid as μ approaches zero. If a controller stabilizes a system model in which these components are assumed rigid, then it also stabilizes the model in which these components are flexible, provided μ is sufficiently small. The results are illustrated by an example