Catastrophes in Control Systems

Catastrophes occur in a control system when a small perturbation of the controller leads to a consierable change in the qualitative properties of the closed loop system. Such a controller is sometimes called "fragile." It is shown in the book that optimal controllers are particularly fragile. The fragility is inherent due to hidden degeneracies arising from the underlying optimization methods. In order to understand fragile controllers, it is useful to first understand fragile matrices and polynomials. The book begins with an examination of fragile polynomials, including the well known Wilkinson polynomial.

The book is written primarily for control engineers, but it should also be of interest to numerical analysts, physicists, economists and others who use matrices and polynomials in computational processes.