H2 performance limitation of a class of nonlinear non-minimum phase systems

In this paper, we study H₂ performance limitation of the nonlinear non-minimum phase systems with a ´new´ structure that the linear combination of all the states of the systems serves as the input of the dynamics where the unstable zero-dynamics is. It is shown that the best attainable tracking performance of the above system is equal as the minimum energy of stabilizing the ´extended´ dynamics which is relevant to all the system´s states except for the state whose differential equation contains the system´s control input explicitly. In the end, we use two examples to illustrate our theorem. The first one is a simple comparison between two systems with different structures and the second one is a more practical object - the aircraft´s longitudinal motion. For the latter one, we derive the H₂ performance limitation of the nonlinear aircraft´s longitudinal motion.