Title
Algebraic and Differential Topology of Robust Stability,Used
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In this book, two seemingly unrelated fields algebraic topology and robust control are brought together. The book develops algebraic/differential topology from an applicationoriented point of view. The book takes the reader on a path starting from a wellmotivated robust stability problem, showing the relevance of the simplicial approximation theorem and how it can be efficiently implemented using computational geometry. The simplicial approximation theorem serves as a primer to more serious topological issues such as the obstruction to extending the Nyquist map, Ktheory of robust stabilization, and eventually the differential topology of the Nyquist map, culminating in the explanation of the lack of continuity of the stability margin relative to rounding errors. The book is suitable for graduate students in engineering and/or applied mathematics, academic researchers and governmental laboratories.
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