Finite-time control based on uncertain linear singular systems with disturbance and time-delay outputs

In this paper, we consider the static output feedback, finite-time disturbance rejection problem for a class of linear singular systems with the time-varying norm-bounded uncertainties and time-delay outputs. The first result provided in this paper is a sufficient condition for finite-time state feedback disturbance rejection in the presence of constant disturbances. This condition requires the solution of an LMI or BMI Therefore, we consider the more general output feedback case, which is shown to be reducible to the solution of an optimization problem involving Bilinear Matrix Inequalities (BMI). Finally, we deal with the case in which the disturbance is time-varying and generated by a linear singular system with outputs.