Changing the fundamental characteristics of the input signal creates various new theoretical challenges in control design.
The problem of input-to-output discontinuity occurs whenever the system input contains nonsmoothness. Such nonsmoothness can come from unintended sources such as shock and high-frequency vibration disturbances, or from necessary control strategies, e.g. when system switches operation modes. The latter is particularly important in switched control due to the fact that a single linear time-invariant (LTI) controller is insufficient in controlling complex systems that exhibit time-varying characteristics or operate under conflicting control requirements.
The input-to-output discontinuity problem creates theoretical and practical barriers in high-performance control and complex systems, due to the potential adverse transient responses induced by the abrupt input changes.
