A course in H∞control theory [Book reviews]

This book offers a stimulating introduction to linear control theory with an H
_∞
-optimality criterion. The general problem dealt with in the book, called the "standard problem," consists of designing a controller which minimizes the H,-norm of a tixed closed-loop transfer matrix. The H
_∞
norm of a transfer matrix is the maximum over all frequencies of its largest singular value. Under suitable hypotheses, the construction of nearly optimal solutions is clearly described. The systems considered are all linear, time-invariant, and finite-dimensional, and they evolve in continuous time. By limiting the discussion to the essential details, Francis' book succeeds in giving a clear picture of a rather involved subject. A reader with a good command of linear system theory and an elementary knowledge of the language of operator theory will find it a good introduction to the H
_∞
area. To the more experienced reader, or to the aspiring researcher in this field, the book can also be useful to point out those aspects of the theory which still need to be developed.