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We study the stability properties of nonlinear discrete-time systems around an invariant periodic manifold. We construct a special set of local coordinates that highlight the tangential and transverse dynamics of the system. Such transverse coordinates play a key role in our analyses. One finds, for example, that an invariant periodic manifold of a discrete time system may contain both stable and...
We propose a nonlinear controller to regulate the swinging energy of the pendulum for a cart and pendulum system. Roughly speaking, the controller is designed to regulate an output (the swing energy) while providing internal stability (regulating the cart position). It is difficult to apply many of the standard nonlinear control design techniques, since the output zeroing manifold does not contain...
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