Robust Dynamic Output Feedback $H_\infty$ Control

Abstract

This chapter deals with the robust dynamic output feedback $H_\infty$ control problem for uncertain linear systems. As a representative, just the discrete-time systems with polytopic uncertainties are considered. First, some basic results on robust dynamic output feedback $H_\infty$ control of the systems are introduced. Then, the LMI decoupling approach is proposed to achieve the design of $H_\infty$ control. Unlike the strategy of change of variables, the proposed results are effective for solving the robust dynamic output feedback $H_\infty$ control problem using the LMI technique. The effectiveness of the proposed design methods is finally demonstrated through a numerical example.