Conditions for mixed small gain and positive real property for LTI systems

The strictly positive real and small gain properties are two of the most important properties in control field. However, in the real world, many practical plants fail to satisfy these properties. In this paper, we propose a new class of systems named “Overlapping Mixed Frequency Property” which is closely related to the mixed small gain and positive real property. A matrix equation related to this property is also constructed and applied to find the stability condition on an output feedback system.