Extension of Stability Radius to Neuromechanical Systems With Structured Real Perturbations

The ability of humans to maintain balance about an unstable position in a continuously changing environment attests to the robustness of their balance control mechanisms to perturbations. A mathematical tool to analyze robust stabilization of unstable equilibria is the stability radius. Based on the pseudo-spectra, the stability radius gives a measure to the maximum change of the system parameters without resulting in a loss of stability. Here, we compare stability radii for a model for human frontal plane balance controlled by a delayed proportional-derivative feedback to two types of perturbations: unstructured complex and weighted structured real. It is shown that: 1) narrow stance widths are more robust to parameter variation; 2) stability is maintained for larger structured real perturbations than for unstructured complex perturbations; and 3) the most robust derivative gain to weighted structured real perturbations is located near the stability boundary. It is argued that stability radii can effectively be used to compare different control concepts associated with human motor control.