Approximate Tracking of Periodic References in a Class of Bilinear Systems via Stable Inversion

This article deals with the tracking control of periodic references in single-input single-output bilinear systems using a stable inversion-based approach. Assuming solvability of the exact tracking problem and asymptotic stability of the nominal error system, the study focuses on the output behavior when the control scheme uses a periodic approximation of the nominal feedforward input signal ud. The investigation shows that this results in a periodic, asymptotically stable output; moreover, a sequence of periodic control inputs un uniformly convergent to ud produce a sequence of output responses that, in turn, converge uniformly to the output reference. It is also shown that, for a special class of bilinear systems, the internal dynamics equation can be approximately solved by an iterative procedure that provides closed-form analytic expressions uniformly convergent to its exact solution. Then, robustness in front of bounded parametric disturbances/uncertainties is achievable through dynamic compensation. The theoretical analysis is applied to nonminimum phase switched power converters.