This paper is concerned with the finite-time projective synchronization problem of fractional-order memristive neural networks (FMNNs) with mixed time-varying delays. Firstly, under the frame of fractional-order differential inclusion and the set-valued map, several criteria are derived to ensure finite-time projective synchronization of FMNNs. Meanwhile, three properties are established to deal with different forms of the finite-time fractional differential inequation, which greatly extend some results on estimation of settling time of FMNNs. In addition to the traditional Lyapunov function with 1-norm form in Theorem 1, a more general and flexible Lyapunov function based on p-norm is constructed in Theorem 2 to analyze the finite-time projective synchronization problem, and the estimation of settling time has been verified less conservative than previous results. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.
This paper is concerned with the finite-time synchronization (FTS) of memristor-based fractional order Cohen-Grossberg neural networks (MFCGNNs) with time-varying delays. Under the frame of fractional order differential inclusion and set-valued map, some new sufficient conditions to guarantee the FTS of MFCGNNs are established by means of constructing two different Lyapunov functions based on L1-norm in Theorem 1 and Lp-norm in Theorem 2. Via applying the asymptotic expansion property of Mittag-Leffler function, we propose a new estimation method of the settling time for synchronization which is less conservative than previous researches. Meanwhile, we deeply discuss the influence factor of settling time for synchronization. Finally, two numerical examples are given to demonstrate the effectiveness of obtained results. INDEX TERMS Memristor-based Cohen-Grossberg neural networks, finite-time synchronization, estimation of the settling time.
This paper presents the finite-time synchronization (FTS) via piecewise control laws for a class of memristive Cohen-Grossberg neural networks (MCGNNs) with time-varying delays. First, based on memristive neural network theory, differential inclusion theory, and stability theory, several new sufficient conditions are established to ensure the FTS stability of a class of MCGNNs with time-varying delays. Then, three control laws are designed. By comparison with a normal control law, the piecewise control law determined by finite-time control (FTC) θ (t) can shorten the settling time. Also, the piecewise control law determined by the dynamic error E(t) and FTC θ (t) can shorten the settling time. Finally, a numerical simulation example is provided to illustrate the effectiveness of the new methods. INDEX TERMS Memristive Cohen-Grossberg neural networks, finite-time synchronization, piecewise control.
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