ABSTRACT
The problem arises of provisioning a limited resource in a distributed manner, without explicit knowledge of the number of agents attempting to share that resource. Moreover the number of agents can grow very large. Such problems can be formulated as optimization problems or as feedback control problems, depending on the application. One issue in the design of such systems is the need to find control algorithms whose actions do not depend on the number of agents participating in the scheme. This independence of the number of agents assures the scalability of the control algorithm. A passive linear time-invariant system is a system whose transfer function is positive real. The notion of a positive real (PR) function and of a strict positive real (SPR) function is important in many areas of engineering systems, in particular in control theory and in circuit theory.
