Strict Global Lyapunov Functions for Mechanical Systems

A novel Lyapunov function is introduced. The author treats the PD compensated mechanical system, which is defined on a configuration space which admits a trivial tangent bundle. Previous results are derived in a simpler form, namely, that such systems are exponentially stable, hence BIBO stable, and steady-state ouptut magnitudes are proportional to input magnitudes with a constant of proportionality depending in a simple fashion on the PD gain magnitudes.

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