Relaxation of output zeroing for bilinear non-minimum phase systems

Linear control design techniques for output setpoint tracking of regulation problems can be extended, through input output feedback linearization (IOFL), to non-linear, input-affine systems, but are not applicable to the case of equilibrium points that exhibit non-minimum phase characteristics. Rather than resort to minimum phase approximations, this paper instead proposes a relaxation of IOFL that does not require IOFL to be implemented at every sampling instant. The relaxation introduces degrees of freedom which, in the case of bilinear systems, can be used efficiently to achieve tracking/regulation, and to maintain this property (to within perturbations caused by the relaxation) until the desired state is reached. A way for expanding the region of attraction is considered and the results of the paper are demonstrated through simulation examples.