Fixed-Time Stability of Nonlinear Impulsive Systems and Its Application to Inertial Neural Networks.

This article is concerned with the fixed-time stability (FTS) problem of nonlinear impulsive systems (NISs). By means of the impulsive control mechanism and Lyapunov functions theory, several sufficient conditions are established to ensure the FTS of general NISs. Meanwhile, some novel impulse-dependent settling-time estimation schemes are developed, which fully considers the influence of stabilizing impulses and destabilizing impulses on the convergence rate of the system states. The proposed schemes establish a quantitative relationship between the upper bound of the settling time and impulse effects. It shows that stabilizing impulses can accelerate the convergence rate of the system states and leads to the upper bound of the settling time being smaller. Conversely, destabilizing impulses can reduce it and make the upper bound of the settling time larger. Then, the theoretical results are applied to delayed inertial neural networks (DINNs), where two kinds of controllers are designed to realize fixed-time synchronization of the considered systems in the impulse sense. Finally, some numerical examples are provided to illustrate the validity of the proposed theoretical results.

Further results on finite-time synchronization of delayed inertial memristive neural networks via a novel analysis method.

In this paper, we propose a novel analysis method to investigate the finite-time synchronization (FTS) control problem of the drive-response inertial memristive neural networks (IMNNs) with mixed time-varying delays (MTVDs). Firstly, an improved control scheme is proposed under the delay-independent conditions, which can work even when the past state cannot be measured or the specific time delay function is unknown. Secondly, based on the assumption of bounded activation functions, we establish a new Lemma, which can effectively deal with the difficulties caused by memristive connection weights and MTVDs. Thirdly, by constructing a suitable Lyapunov functions and using a new inequality method, novel sufficient conditions to ensure the FTS for the discussed IMNNs are obtained. Compared with the existing results, our results obtained in a more general framework are more practical. Finally, some numerical simulations are given to substantiate the effectiveness of the theoretical results.