Low-frequency limitations in saturated and delayed networked control

The paper analyzes a continuous time nonlinear networked control system where delay and saturation are main effects. These effects occur e.g. in control of flow of a general quantity from a source node to a sink node. The flow is one-directional, meaning that there is a saturation between the nodes that limits the flow to be positive and below a maximum value. The controlled plant is located in the sink node and the controller is located in the source node. The plant and the controller are modeled by linear filters parameterized with poles and zeros. Feed-forward control from a measured disturbance is included. Delays affect both the downlink control signal and the uplink measurement signals. The paper proves that for large delays, L₂-stability does not follow from the Popov criterion unless the quotient of the products of all zeros and the product of all poles in the feedback path is less than 1/kG_p, where k is the slope of the saturation and G_p is the gain constant of the loop gain. In case the plant models a leaky reservoir, the conclusion is that the amount of low frequency gain of the controller cannot be arbitrarily high at the same time as the amount of leakage of the reservoir is arbitrarily low. For data flow control in communications this means that an increased requirement to regulate static errors of the data queue needs to be accompanied by a reduced capacity.