Control allocation and zero dynamics

Closed-loop stability for dynamic inversion controllers depends on the stability of the zero dynamics. The zero dynamics,however, depend on a generally nonlinear control allocation function that optimally distributes redundant controls. Therefore, closed-loop stability depends on the control allocation function. A sufficient condition is provided for globally asymptotically stable zero dynamics with a class of admissible nonlinear control allocation functions. It is shown that many common control allocation functions belong to the class of functions that are covered by the aforementioned zero dynamics stability condition. Aircraft flight control examples are given to demonstrate the utility of the results.