A Frequency Domain Approach for Systems with Slow and Fast Modes

Many systems to which modern automatic control techniques are applied exhibit multiple time scale behavior. Recent work has shown that the control task can be simplified through model reduction or decomposition methods which rely on such behavior. Application of modern control methods to complicated system models can lead to complicated or oversensitive controllers. The authors show why decomposition of control problems into slow and fast portions is justified and present some theorems relating to the problem. Most decomposition and reduction methods employ singular perturbation theory as their mathematical basis. This paper approaches the problem from a frequency-domain viewpoint.