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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.