Energy-Balance PBC of nonlinear dynamics under sampling and delays

The paper provides a new class of passivity-based controllers (PBCs) for stabilizing sampled-data input-delayed dynamics at a desired equilibrium via energy-balancing (EB) and reduction. Given a nonlinear dynamics under piecewise constant and retarded input, we first exhibit a new dynamics (the reduced dynamics) that is free of delays and equivalent to the original one. Accordingly, we design the digital controller assigning a suitable energetic behaviour to the reduced delay-free model with a stable target equilibrium. Then, it is proved that such a controller solves the EB-PBC problem on the original retarded system. The results are illustrated over a simple mechanical system.