Francis B.A. A Course in H_infinity Control Theory

Springer Verlag, Berlin, 1987. — 159 p. — ISBN: 3-540-17069-3.
Aim of this book is to give an elementary treatment of linear control theory with an H-infinity optimality criterion. The systems are all linear, time-invariant, and finite dimensional and they operate in continuous time. The book has been used in a one semester graduate course, with only a few prerequisites: classical control theory, linear systems (state-space and input-output viewpoints), and a bit of real and complex analysis.
Only one problem is solved in this book: how to design a controller which minimizes the H-infinity norm of a pre-designated closed-loop transfer matrix. The H-infinity norm of a transfer matrix is the maximum over all frequencies of its largest singular value. In this problem the plant is fixed and known, although a certain robust stabilization problem can be recast in this form. The general robust performance problem - how to design a controller which is H-infinity optimal for the worst plant in a pre-specified set - is as yet unsolved.