In control system analysis and design the first step is to produce a mathematical model of the system being controlled. This model includes not only the dynamic equations of the system but also a characterization of any disturbances affecting the system. If the model is assumed to be exact and the disturbances are assumed to be Gaussian, then the control that minimizes the expected value of a quadratic form in the errors is given as the LQG (Linear Quadratic Gaussian) controller. However such LQG controller is not robust; small perturbations of the dynamics may produce unstable closed-loop behavior. In order to avoid such undesired outcome one has to incorporate the uncertainty of the model dynamics explicitly in the controller design. A nowadays standard way of measuring both the disturbance signal gains and the plant uncertainties is given by the so- called H-infinity norm and thus H-infinity optimal control methods form an essential feature in synthesizing useful robust controllers. Also structured plant uncertainties give rise to a particular H-infinity optimal control related to structured uncertainties. In general any of the possible H-infinity optimal control problems centers around the characterization of controllers producing a bounded (in the H-infinity norm) closed loop transfer. All such controllers may be viewed as a ball in some H-infinity controller space and a natural question is then to decide about which element from this ball has to be chosen. The book is chosing this controller as a controller that minimizes an entropy integral of a transfer function. In this context entropy is a system theoretic notion for information measure or the entropy from spectral theory. In fact this minimal entropy-integral-controller can be shown to produce an upper bound on the more standard LQG cost. A detailed development of the minimum entropy solution in the H-infinity optimal control problem, exploiting state space techniques, is the control problem of the monograph.

Reviewer: H.Nijmeijer