Linear quadratic control and frequency domain inequalities

Abstract

In the state-space approach to the H _∞-control problem the linear quadratic control problem (LQ-problem) plays an important role. In Chapter 4 we relate the H _∞-control problem with state-feedback to a certain sup-inf-problem, which can be solved using the LQ-theory of this chapter. In some sense the Riccati equations corresponding to the solution of the H _∞-control problem are reminiscent of the LQ-Riccati equations. The results in this chapter also have applications to other system theoretical problems, such as questions arising in optimal control, identification theory, and robust stability theory (positive real lemma, bounded real lemma and so on). Therefore this chapter can be considered as an entity, interesting in its own right.