G . Bastin and A . Provost Feedback stabilisation with positive control of dissipative compartmental systems

In many process control applications, the system under consideration is compart-mental and positive. This means that the system satisfies a mass conservation condition and that both the state variables and the control input are physically constrained to remain non-negative along the system trajectories. For such systems, the design of state feedback controllers makes sense only if the control function is guaranteed to provide a non-negative value at each time instant. The purpose of this paper is to present a positive control law for the feedback stabilisation of a class of positive compartmental systems which are dissipative but can nevertheless be globally unstable. The approach is illustrated with an application to the control of an industrial grinding circuit.