Gabriele Oliva, Stefano Panzieri and Roberto Setola, "Discrete-Time Linear Systems with Fuzzy Dynamics," Journal of Intelligent & Fuzzy Systems, In Press. [url]
This paper analyzes linear discrete-time dynamic systems where both state variables and model coefficients are represented by fuzzy numbers. Since fuzzy numbers are not a closed group with respect to multiplication, the evolution of a system with fuzzy dynamic parameters can not be directly obtained in a closed form. To overcome this limit the systems have to be analyzed in terms of admissible solutions, hence the analysis has to be performed in the framework of Fuzzy Difference Inclusions. The evolution of such systems, while easy to characterize in the case of non-negative coefficients, becomes more complex for general systems, and in this paper the general problem is addressed resorting to an internally positive realization of the system.