ABSTRACT
It is a compelling idea to conjure a stable, or robust, state out of an unstable state or combination of unstable states. In a natural way, this can be formulated as a problem in control theory: how can an instability be controlled to produce a stable state? A well-known example is the inverted pendulum. Kapitza (see [12]) showed that a vertically oscillating pivot can produce a stable pendulum that is upside down. This control strategy can be construed as placing the pendulum in a stable state (the vertical acceleration can overcome gravity on the way down) for part of the time. The pendulum is thus switching between a stable and an unstable state and the stable state wins. This suggests an interesting question: can switching between unstable states induce stability? This question can be answered positively with a system that jumps between two saddles, in a time-dependent way, in such a way that the saddles switch stable and unstable directions. As soon as the system moves off in the unstable direction, the switch makes that direction stable and so on. This can be implemented as a control strategy but it remains another question whether this mechanism is found in specific applications.
