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On the set stabilization problem in control theory

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by Manfredi Maggiore, University of Toronto

Motivated by examples from Engineering, Physics, and Biology, we
discuss the set stabilization problem in control theory: given a
control system (a system of ODE's with inputs) find, if possible, a
smooth input function stabilizing the system's state to an embedded
submanifold of the state space. An approach to solving this problem is
to decompose the system dynamics into components tangential and
transverse to the manifold in question and find conditions for the
transverse dynamics to be linear, for then a wealth of techniques from
linear control theory can be applied to solve the original problem. We
present necessary and sufficient conditions for the transverse
dynamics to be linear and discuss simple examples.