Mittag-Leffler Stabilization Research Articles

Global Mittag–Leffler stabilization of fractional-order complex-valued memristive neural networks

This paper presents the theoretical results about global Mittag–Leffler stabilization for a class of fractional-order complex-valued memristive neural networks with the designed two types of control rules. As the extension of fractional-order real-valued memristive neural networks, fractional-order complex-valued memristive neural networks have complex-valued states, synaptic weights, and the activation functions. By utilizing the set-valued maps, a generalized fractional derivative inequality as well as fractional-order differential inclusions, several stabilization criteria for global Mittag–Leffler stabilization of fractional-order complex-valued memristive neural networks are established. A numerical example is provided here to illustrate our theoretical results.

Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

In this paper, we consider the problem of Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients. With the help of backstepping design method, the stabilizing functions and tuning functions are constructed. The controller is designed to ensure that the pseudo-state of the fractional-order nonlinear system converges to the equilibrium. The effectiveness of the proposed method has been verified by some simulation examples.

Global Mittag-Leffler Stabilization of Fractional-Order Memristive Neural Networks.

According to conventional memristive neural network theories, neurodynamic properties are powerful tools for solving many problems in the areas of brain-like associative learning, dynamic information storage or retrieval, etc. However, as have often been noted in most fractional-order systems, system analysis approaches for integral-order systems could not be directly extended and applied to deal with fractional-order systems, and consequently, it raises difficult issues in analyzing and controlling the fractional-order memristive neural networks. By using the set-valued maps and fractional-order differential inclusions, then aided by a newly proposed fractional derivative inequality, this paper investigates the global Mittag-Leffler stabilization for a class of fractional-order memristive neural networks. Two types of control rules (i.e., state feedback stabilizing control and output feedback stabilizing control) are designed for the stabilization of fractional-order memristive neural networks, while a list of stabilization criteria is established. Finally, two numerical examples are given to show the effectiveness and characteristics of the obtained theoretical results.

Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks

In this paper, stabilization control of fractional-order bidirectional associative memory neural networks is formulated and studied. By estimating Mittag-Leffler function and some novel analysis techniques of fractional calculation, a generalized Gronwall-like inequality of Caputo fractional derivative is established. Then by applying Lyapunov approach, linear state feedback control law and partial state feedback control law are presented to stabilize the fractional-order bidirectional associative memory neural networks. This analysis framework can be applied to closed-loop control of fractional-order systems. A numerical example is given to show the effectiveness of the derived results via computer simulations.