My aim in 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.

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