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This volume represents an overview of some recent developments on the absolute stability of nonlinear systems. The contents are divided into six chapters - chapter 1 introduces the main tools and the principal results used in this text, such as Liapunov functions, K-class functions, Dini-derivatives, M-matrices and the principal theorems on global stability.
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.