Robust control of systems with unstable zero-dynamics

An important feature of systems with unstable zero-dynamics is that there exist unstable modes. Unstable zero-dynamics is related to the unstable modes, but are not the same with each other. Unstable zero-dynamics is invariant, but the unstable modes can be stabilized. With composite control, a fast loop is employed to directly stabilize the unstable subsystem. The slow loop formed from the output is then designed by existing robust method, while the dynamics of the fast loop is treated as the unmodeled dynamics. The whole design is robust. An example of an inverted pendulum on a cart is presented to illustrate the design process.