Controlling Uncertain Systems within a Subset of the State Space

In previous work, stabilizing controllers were developed for uncertain systems whose state space is Rⁿ. Here, we present stabilizing controllers for uncertain systems whose state space is some open subset of Rⁿ or for which it is desired to keep all state motions within some open subset of Rⁿ. The controllers, whose construction is based on Lyapunov theory, are, in general, nonlinear. Their use is illustrated by an example.