Exponential and fixed‐time stabilization of memristive neural networks with mixed delays

In this paper, we investigate the problem of fixed-time stabilization (FTS) for a class of second-order nonlinear time-delay systems. Using the fixed-time stability theory and Lyapunov-Krasovskii functional, a design scheme of fixed-time stability for time-delay systems is proposed. This scheme effectively solves the adverse impact of time-delay on the system, and and ensure that the corresponding closed-loop system is stable for a fixed time. The main benefit of the proposed control methods is that the influences of time-delay state and nonlinear uncertainties can be effectively attenuated with the help of feedback method. Finally, the simulation is given to show the effectiveness of the design scheme.

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Fixed‐time stabilization for a class of nonlinear time‐delay systems

Wang

Peng

Xie

2023

“…However, the dynamic behaviors of NNs are closely related to all successful applications. As stability is a key aspect in the construction of NNs, many researchers have studied the stability of NNs and have come up with some interesting results, see references [4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Robust stability of uncertain stochastic switched inertial neural networks with time‐varying delay using state‐dependent switching law

Banu¹,

Banupriya²,

Krishnasamy

et al. 2023

In this paper, the problem of robust stability analysis for a type of uncertain stochastic switched inertial neural networks (SSINNs) with time-varying delay is investigated. First, the original second-order system is converted into first-order differential equations using the variable transformation method. Next, some sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained using Lyapunov-Krasovskii functional (LKF), state-dependent switching (SDS) method, and Jensen's integral inequality for estimating integral inequalities so that the augmented system is robust, global, and asymptotically stable in the mean square for the uncertain SSINNs with time-varying delay. It is shown that the stability of the above considered system composed of all unstable subsystems can be achieved by using the SDS law. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed SDS law.

“…It should be pointed out that in the general stability simulation of the neural networks, the system trajectory always evolve from the initial value to the final result to be a black box. That is, these existed literatures (see earlier studies [36–39]) only focus on stable results but ignore process control. To overcome the limitation, in the process of exponential stability analysis, we put forward a trajectory similarity approach via system state and sampling trajectory, that is,

normal𝔼 {(‖‖, x false(t false) - \overset{x}{true} ((), ([], \frac{t}{σ}) σ))}^{2} = φ normal𝔼 false‖ x false(t false) {false‖}^{2}, false(φ > 0

is a constant).…”

Section: Introductionmentioning

confidence: 99%

Stability analysis based on a control adjuster for switched neural networks by trajectory similarity

Zhou

Zhang

2023

This paper focuses on a class of exponential stability control problem for the stochastic neural networks (SNNs) with time‐varying delays and Markov jump (TVDMJ). As a prerequisite to the main theorem, the existence and uniqueness of the solution for the main system are proved via contraction map principle. For the stability control of the system, we design a controller which can be adjusted the parameters to make the system stabilization. We use this controller to actively control the stability behavior of the system, rather than the papers by setting the appropriate parameters to make the system achieve a stable state. Based on the intermittent control, we design a novel trajectory similarity process control and obtain exponential stability results, which are less conservative than the existing theoretical results. Two examples based on some numerical calculation and simulation diagrams are presented to validate the effectiveness for the utilized techniques.