ABSTRACT
In this chapter, we study some basic H∞ and H2 problems. These include the H∞ and H2 state feedback control, and also the robust H∞ and H2 control problems.
The results in this chapter are closely related to the stability analysis results covered in Chapter 5. In Chapter 5, we have given the analysis conditions for the H∞ and H2 indices of a linear system to be bounded by certain level. But in this chapter, we will first apply those conditions to the closed-loop system of the state feedback control system and then, through a variable substitution, turn the design conditions for H∞ and H2 control into LMIs, and meanwhile get the expression of the gain matrix. Such a procedure is shown in Figure 8.1.
