On the Switching Controllers' Issue

The paper is discussing the dangerous instability that may occur in the switching controllers' case. This phenomenon cannot be treated by the conventional frequency analysis because of the non-null initial conditions. The qualitative phase trajectory analyze of the difference between the controllers outputs is used instead. The second and the fourth quadrants of the phase plane are recommended for switching, while the first and the third quadrants must be avoided. An analogy with the sliding mode method is proposed and three workbench studies are provided. The phenomenon is framed into the Postmodernist context.