H-infinity control applications

The focus of the chapter is on a part of control theory called H-infinity control. The problem involved is the general H-infinity control problem, the so-called standard problem. It concerns the construction of a stabilizing controller with additional constraints on the maximum of the norm of the closed loop transfer function, taken over the values of the argument on the imaginary line. In its simplest form the problem is equivalent to the rational matrix Nehari problem considered in Chapter 18. The label H-infinity is related to the fact that a proper rational matrix function is stable if and only if it is analytic and uniformly bounded in the open right half plane. A function with the latter properties is usually referred to as an H∞-function (on the right half plane).