  The analytical background of nonlinear observers based on minimal energy
estimation is discussed. It is shown that locally the derivation of the
observer equation based on a trajectory with pointwise minimal energy can be
done rigorously. The result is obtained by a local sensitivity analysis of the
value function based on Pontryagin's maximum principle and the
Hamilton-Jacobi-Bellman equation. The consideration of a differential Riccati
equation reveals that locally the second derivative of the value function is a
positive definite matrix. The local convexity ensures existence of a trajectory
minimizing the energy, which is then shown to satisfy the observer equation.
