Abstract
Sufficient conditions for non-oscillating responses of a relay-controlled composite system are studied. We find a typical example in the VQ control of an electric power system, where non-oscillating responses of the controlling switches are desired. The realys considered have dead regions, multi-inputs and the following properties: The space of the input variables to the relay is devided into a finite number of regions, while the output of the relay is constant for the inputs which belong to the same region. The non-oscillating trajectory is defined to be a trajectory which does not pass a pair of regions defined as opposite. Assume that every trajectory of isolated subsystems which starts from an initial point belonging to some area is non-oscillating. The trajectories of the composite system may be supposed also nonoscillating if the subsystems are weakely coupled. Evaluating the upper bound of interference that a subsystem receives from other subsystems, the conditions for non-oscillating responses are obtained. The results may also applicable as stability criteria for the systems of which Lyapounov functions are difficult to find.
