Robust Observer-Based Output Feedback $H_\infty$ Control

Abstract

This chapter studies observer-based output feedback $H_\infty$ control problem for discrete-time linear systems with polytopic uncertainties and norm bounded uncertainties. For systems with polytopic uncertainties, the descriptor systems approach is used to design observers and controllers. For systems with norm bounded uncertainties, in the so-called two-step procedure, a selective approach is introduced first, in which results of the first step are allowed to be selected in order to reduce the conservatism of previous approaches. Then, a simple LMI result for observer-based output feedback $H_\infty$ control design for uncertain linear systems with a special case is given. Finally, the LMI decoupling approach is also considered for designing observers and controllers.