General matching conditions in the theory of controlled Lagrangians

Gives necessary and sufficient conditions for matching and generalized matching and sufficient criteria for stabilizability by the generalized matching method. A few examples are given, including an inverted pendulum on a cart. It is probably straight forward to extend the methods given here to wider classes of problems, including Lagrangians with vector potential terms, affine conditions on the admissible controls (allowing for systems with inner dissipation) and nonholonomic constraints.

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