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On finite-time control of inner systems

It is well known that non-minimum phase zeros of dynamical systems restrict the achievable performance of closed-loop transfer functions. If performance is specified in terms of finite time properties, then it is not evident that the zero structure of transfer functions limits the achievable performance of the controlled system. It is shown that the Hankel singular values of the inner factor of the system transfer function provide relevant information for achievable (finite time) performance of the controlled process.