A Simple Architecture for Arbitrary Interpolation of State Feedback

Stability of a linear system under fast switching or blending of a set of controllers can be ensured by an appropriate observer-based state-space realization. In this letter, the more specific problem is considered of arbitrary interpolation of a set of state feedback gains based on an initial static state feedback. First, the dynamic augmentation generating this parameterization is derived as well as the associated parameters for local recovery of predefined static controllers. By further simplification, a simple and intuitive structure is obtained with only a single design matrix. We propose to exploit this remaining degree of freedom to maximize robustness in terms of coprime factor uncertainty. The resulting parameterization is comparatively simple to implement in both continuous and discrete time. The robotics problem of active variable impedance control serves to illustrate utility of this parameterization.