The main topic of the book is closed-loop design and the computation of performance limits using convexity. The book introduces a standard framework for the control design problem and describes many practical design specifications in this framework. It is shown that many of these specifications are closed-loop convex; the corresponding control design problems can therefore be cast as infinite-dimensional nondifferentiable convex optimization problems. The book shows how these problems can be solved using the ellipsoid and cutting-plane algorithms, using a Ritz approximation.

The book describes how the achievable performance can be computed numerically for any family of closed-loop convex specifications. Closed-loop convex specifications include, for example, H-two, H-infinity, or l-one norm bounds, entropy bounds, step response envelopes and asymptotic command decoupling.

The book contains many previously unpublished results. The clear exposition and numerous examples make the material accessible to a wide audience, including researchers, graduate students and industrial control engineers. The book includes standalone chapters covering norms of signals and systems, and their computation, as well as standalone chapters covering convex analysis and nondifferentiable convex optimization.

Over 27000 lines of matlab source were written to generate the numerical examples and 216 plots and figures. To the authors' knowledge, the extent of the numerical computation in this book is unprecedented in a book on control systems.

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