Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment

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Analysis of the energy‐based swing‐up control of the Acrobot (2007, background): “It is well known that if an unstable equilibrium point is hyperbolic, that is, the Jacobian matrix evaluated at that point has no eigenvalues on the imaginary axis, then the set of initial conditions converging to the equilibrium point is of Lebesgue measure zero [10].”
Nonlinear control systems - A brief overview of historical and recent advances (2017, methodology): “Model predictive heuristic control [35] 1980s Zames Formulation of H∞ control [36] 1989 Ortega and Spong Concept of Passivity Based Control (PBC) [37] 1990 – Start of ’activation process’ 1990s Sontag and Wang Theory of input-to-state stability for nonlinear systems [38] 1995 Isidori Geometric contr”
Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems (2008, background): “Some simple calculations show that (43) becomes , which is known as the potential energy matching equation [3], [ 25 ].”
Nonprehensile Dynamic Manipulation: A Survey (2018, methodology): “based on an interconnection and damping assignment (IDA) is applied in [80], modifying both the related potential and kinetic energies.”