Synchronization Control of Riemann-Liouville Fractional Competitive Network Systems with Time-varying Delay and Different Time Scales

This paper is concerned with a class of Riemann-Liouville fractional-order competitive neural networks with time-varying delay and different time scales. Based on delay-partitioning approach, we construct two suitable Lyapunov functionals including fractional integral terms, respectively, and avoid computing their fractional-order derivatives to derive the synchronization conditions. The sufficient conditions are proposed to ensure the complete synchronization between fractional-order response system and fractional-order derive system. By solving the algebraic equalities or linear matrix inequalities (LMIs), the design of the gain matrix of the linear feedback controller can be realized. An illustrative example is also presented to show the validity and feasibility of the theoretical results.