A regulator stabilization technique: Kumar-Seidman revisited

We discuss the stability of a class of models applicable to manufacturing systems consisting of several machines, producing many types of parts, sharing resources, under dynamical decentralized scheduling. Kumar and Seidman (ibid., vol. 35, no. 3, p. 289-98, 1990) have shown the role of “cycles” of material flow as a source of instability, presented sufficient conditions for stability and also presented a general supervisory mechanism to ensure stability. In this note, we exploit the hereditary properties of the sufficient conditions for stability (hereditary in the connection graph that models the interconnections), relax this condition and also present a regulator based stabilization technique, easily implementable in distributed fashion. Besides that, as a corollary, we give an upper bound for the number of regulatory mechanisms to be used in a given system. This upper bound is also valid for previous stabilization techniques and for the universally stabilizing supervisory mechanism