H∞ balancing for nonlinear systems

In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H∞ control problem for nonlinear systems we define H∞ balancing. Furthermore, we investigate the monotonicity of the Hamilton-Jacobi-Bellman equations that appear in this balancing method. The method is used as a tool for model reduction.