Gabriele Oliva, Stefano Panzieri and Roberto Setola, "Distributed Synchronization Under Uncertainty: a Fuzzy Approach," Fuzzy Sets and Systems, Elsevier eds., vol. 206, pag. 103-120, 2012. (doi:10.1016/j.fss.2012.02.003)
In this paper the Synchronization of systems with fuzzy initial conditions is introduced, as a convenient framework to obtain a shared estimation of the state of a system based on partial and distributed observations, in the case where such a state is affected by ambiguity and/or vagueness. After discussing the synchronization of crisp systems, providing a criteria to find a stabilizing control law, the Discrete-Time Fuzzy Systems (DFS) are introduced as an extension of scalar fuzzy difference equations. Besides providing a stability condition for a general DFS, in the linear case it is proven that, under a non-negativity assumption for the coefficients of the system, the fuzzyfication of the initial conditions does not compromise the stability of the crisp system. A framework for the synchronization of arrays of linear DFS is then introduced, proving that the crisp synchronization is a particular case of the proposed approach. Finally, a case study in the field of Critical Infrastructure Protection is provided.