In this book, two seemingly unrelated fields -- algebraic topology and robust control -- are brought together. The book develops algebraic/differential topology from an application-oriented point of view. The book takes the reader on a path starting from a well-motivated 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, K-theory 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.
Chevalia is an enchanted island where ponies and horses rule, its magic powered by eight golden horseshoes hanging in the royal castle-thanks to Pippa and Princess Stardust's efforts to find them all. Her task complete, Pippa has returned to our world . . . but her friends in Chevalia are never far away.
In A Special Surprise, Princess Stardust has come all the way from Chevalia to cheer Pippa on in her first big competition. But when Pippa arrives at the stables, her riding school pony friends are nowhere to be found. Stardust has an idea who is responsible . . . but for the show to go on, Pippa and Stardust must return to Chevalia! Offering a brand new mystery and black and white illustrations throughout, this winning combination of princesses, ponies and collectible jewelry is sure to enchant readers.