Approximate tracking of periodic references in a class of bilinear systems via stable inversion

Abstract

This article deals with the tracking control of periodicreferences in single-input single-output bilinear systems using astable inversion-based approach. Assuming solvability of the exacttracking problem and asymptotic stability of the nominal errorsystem, the study focuses on the output behavior when the controlscheme uses a periodic approximation of the nominal feedforwardinput signal $u_d$. The investigation shows that this results in aperiodic, asymptotically stable output; moreover, a sequence ofperiodic control inputs $u_n$ uniformly convergent to $u_d$produce a sequence of output responses that, in turn, convergeuniformly to the output reference. It is also shown that, for aspecial class of bilinear systems, the internal dynamics equationcan be approximately solved by an iterative procedure thatprovides of closed-form analytic expressions uniformly convergent toits exact solution. Then, robustness in the face of boundedparametric disturbances/uncertainties is achievable throughdynamic compensation. The theoretical analysis is applied tononminimum phase switched power converters.