Control of thermodynamical system with input-dependent state delays

We consider control of a cooling system with several consumers that require cooling from a common source. The flow feeding coolant to the consumers can be controlled, but due to significant physical distances between the common source and the consumers, the coolant flow takes a non-negligible amount of time to travel to the consumers, giving rise to input-dependent state delays. We first present a simple bilinear model of the system, followed by a state feedback control design that is able to stabilize the system at a chosen equilibrium in spite of the delays. We also present a heuristic, performance-oriented improvement to the design. The strategy is illustrated with some simulation examples.