Global Tracking Passivity-based PI Control of Bilinear Systems and its Application to the Boost and Modular Multilevel Converters∗

This paper deals with the problem of trajectory tracking of a class of bilinear systems with time-varying measurable disturbance, namely, systems of the form x(t)=[A + i ui(t)Bi]x(t)+ d(t). We identify, via a linear matrix inequality, a set of matrices {A, Bi} for which it is possible to ensure global tracking of (admissible, differentiable) trajectories with a simple linear time-varying PI controller. Instrumental to establish the result is the construction of an output signal with respect to which the incremental model is passive. The result is applied to the boost and the modular multilevel converter for which experimental results are given.