Synchronization of T–S Fuzzy Fractional-Order Discrete-Time Complex-Valued Molecular Models of mRNA and Protein in Regulatory Mechanisms with Leakage Effects.

This paper addresses the problem of Mittag-Leffler synchronization of T–S fuzzy fractional-order discrete-time complex-valued molecular models of mRNA and protein in regulatory mechanisms with two kinds of regulation functions, respectively. A novel approach is proposed to effectively deal with the joint effects from leakage delay and time varying delay for the class of T–S fuzzy fractional-order discrete-time complex-valued genetic regulatory networks (FDTCVGRNs). By employing Lyapunov stability method and Caputo fractional difference inequalities, several effective conditions according to algebraic inequality and complex-valued linear matrix inequalities are deduced to guarantee the synchronization of the addressed FDTCVGRNs. Moreover, Mittag-Leffler synchronization problem of the nonlinear regulation function in complex-valued molecular models on the basis of general regulation function and linear threshold one. Compared with existing results in the literature, our results are less conservative than existing ones. Finally, simulation results with two numerical examples are demonstrated, which proves the validity of the proposed method. [ABSTRACT FROM AUTHOR]