  In this paper, we introduce a novel class of neural differential equation,
which are intrinsically Lyapunov stable, exponentially stable or passive. We
take a recently proposed Polyak Lojasiewicz network (PLNet) as an Lyapunov
function and then parameterize the vector field as the descent directions of
the Lyapunov function. The resulting models have a same structure as the
general Hamiltonian dynamics, where the Hamiltonian is lower- and upper-bounded
by quadratic functions. Moreover, it is also positive definite w.r.t. either a
known or learnable equilibrium. We illustrate the effectiveness of the proposed
model on a damped double pendulum system.
