In this paper we analyze the functioning of multi-agent robotic systems with decentralized control in conditions of destructive information influences from robots-saboteurs. We considered a type of hidden attacks using interception of messages, formation and transmission of misinformation to a group of robots, and also realizing other actions which have no visible signs of invasion into a group of robots. We analyze existing models of information security of the multi-agent information system based on a measure of trust, calculated in the course of interaction of agents. We suggest a mechanism of information security in which robots-agents produce levels of trust to each other on the basis of the situation analysis developing on a certain step of an iterative algorithm with the use of onboard sensor devices. For improving the metric of likeness of objects relating to one category ("saboteur" or "legitimate agent") we suggest an algorithm to calculate reputation of agents as a measure of the public opinion created in time about qualities of robots of the category "saboteur" in a group of legitimate robots-agents. It is shown that inter-cluster distance can serve as a metric of quality of trust models in multi-agent systems. We give an example showing the use of the developed mechanism for detection of saboteurs in different situations in using the basic algorithm of distribution of targets in a group of robots.