Linear Matrix Inequalities in System and Control Theory
Abstract¶
In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.
Summary¶
Presents linear matrix inequalities as a unifying modeling language for robust control, Lyapunov analysis, controller synthesis, and related system-theory problems. The book helped move control design toward convex optimization by showing that many previously separate problems reduce to tractable LMI and quasiconvex formulations.
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