Robust Output Feedback Control

Abstract

In this chapter, we consider three types of possible linear feedbacks using only the current output information: static feedback proportional to the output measurable signal, observer-based feedback proportional to the state estimation vector, and full-order linear dynamic controllers. For each type of possible linear feedback, we suggest that one characterize the set of all stabilizing gain-feedback matrices by a system of the corresponding linear matrix inequalities, providing the boundedness of all possible trajectories of every controlled plant from the considered class of uncertain systems. We also suggest selecting the optimal feedback gain matrix from the described class of stabilizing feedbacks as the one that minimizes the “size” of the attractive ellipsoid containing all possible bounded dynamic trajectories. The corresponding numerical procedures for designing the best feedback gain matrices are introduced and discussed for each type of considered feedback. Several illustrative examples clearly show the effectiveness of the suggested technique.