A novel and original distributed reputation mechanism is here proposed for a class of networked systems characterized by two distinct groups of nodes: user agents and service providers (servers/resources). The proposed methodology is in charge of intercepting those resources that have the highest quality of service (QoS) on the basis of their reputation (trust) shared among agents. Such a reputation may change over the time mainly influenced by changing performance indexes and other events. As a result, it is shown that the trust evolution can be modeled as the output of a positive switching linear system. This model straightforwardly allows one to prove trust boundedness and other relevant steady-state properties. To illustrate the benefits of this approach, a sensors selection problem for state estimation is outlined and addressed within the proposed framework. In particular, it is formally proved that the resulting estimation scheme ensures, over the time, the selection of the sensor with the current best perceived QoS in a finite time.