Finite-Time Synchronization of Memristive Neural Networks with Proportional Delay

Discontinuous Event-Triggered Control for Local Stabilization of Memristive Neural Networks With Actuator Saturation: Discrete- and Continuous-Time Lyapunov Methods

In this article, the local stabilization problem is investigated for a class of memristive neural networks (MNNs) with communication bandwidth constraints and actuator saturation. To overcome these challenges, a discontinuous event-trigger (DET) scheme, consisting of the rest interval and work interval, is proposed to cut down the triggering times and save the limited communication resources. Then, a novel relaxed piecewise functional is constructed for closed-loop MNNs. The main advantage of the designed functional consists in that it is positive definite only in the work intervals and the sampling instants but not necessarily inside the rest intervals. With the aid of extended reciprocally convex combination lemma, generalized sector condition, and some inequality techniques, two local stabilization criteria are established on the basis of both the discrete- and continuous-time Lyapunov methods. The proposed analysis technique fully takes advantage of the looped-functional and the event-trigger mechanism. Moreover, two optimization schemes are, respectively, established to design the control gain and enlarge the estimates of the admissible initial conditions (AICs) and the upper bound of rest intervals. Finally, some comparison results are given to validate the superiority of the proposed method.

Finite-time H∞ synchronization control for coronary artery chaos system with input and state time-varying delays

This is the first time for studying the issue of finite-time H_∞ synchronization control for the coronary artery chaos system (CACS) with input and state time-varying delays. Feedback control is planned for finite-time of synchronization CACS. By constructing the Lyapunov-Krasovskii functional (LKF) is derived for finite-time stability criteria of CACS with interval and continuous differential time-varying delays. We use Wirtinger-based integral inequality to evaluate the upper bound of the time derivative of the LKF. We apply the single integral form and the double integral form of the integral inequality, according to Wirtinger-based integral inequality, to ensure that the feedback controller for synchronization has good performance with disturbance and time-varying delay. The new sufficient finite-time stability conditions have appeared in the form of linear matrix inequalities (LMIs). Numerical checks can be performed using the LMI toolbox in MATLAB. A numerical example is presented to demonstrate the success of the proposed methods. This resultant is less conservative than the resultants available in the previous works.