Stability and Linearization of Multi-valued Nonlinear Feedback Shift Registers

In this paper, we study stability and linearization of multivalued nonlinear feedback shift registers which are considered as logic networks. First, the linearization of multi-valued nonlinear feedback shift registers (NFSRs) is discussed, which is to find their state transition matrices by considering it as a logical network via a semi-tensor product approach. For a multi-valued NFSR, the new state transition matrix which can be simply computed from the truth table of its feedback function is more explicit. Second, based on the linearization theory of multi-valued NFSRs, we investigate the stability of multi-valued NFSRs, and some sufficient and necessary conditions are provided for globally (locally) stable multi-valued NFSRs. Finally, some examples are presented to show the effectiveness of the proposed results.