A New LMI Approach to Finite and Fixed Time Stabilization of High-Order Class of BAM Neural Networks with Time-Varying Delays

A novel fixed-time stability lemma and its application in the stability analysis of BAM neural networks

In this paper, we put forward an interesting fixed-time (FXT) stability lemma, which is based on a whole new judging condition, and the minimum upper bound for the stability start time is obtained. In the new FXT stability lemma, the mathematical relation between the upper bound of the stability start time and the system parameters is very simple, and the judgment condition only involves two system parameters. To indicate the usability of the new FXT stability lemma, we utilize it to study the FXT stability of a bidirectional associative memory neural network (BAMNN) with bounded perturbations via sliding mode control. To match the developed FXT stability lemma, novel sliding mode state variables and a two-layer sliding mode controller are designed. According to the developed FXT stability lemma, the perturbed BAMNN can achieve FXT stability under the devised sliding mode controller. The upper bound of the stability start time can be calculated easily by virtue of the control parameters, and the sufficient conditions guaranteeing that the perturbed BAMNN can achieve FXT stability have also been derived. Last, we provide some confirmatory simulations.

Distributed adaptive fixed-time neural networks control for nonaffine nonlinear multiagent systems

This paper, with the adaptive backstepping technique, presents a novel fixed-time neural networks leader–follower consensus tracking control scheme for a class of nonaffine nonlinear multiagent systems. The expression of the error system is derived, based on homeomorphism mapping theory, to formulate a set of distributed adaptive backstepping neural networks controllers. The weights of the neural networks controllers are trained, by an adaptive law based on fixed-time theory, to determine the adaptive control input. The control algorithm can guarantee that the output of the follower agents of the system effectively follow the output of the leader of the system in a fixed time, while the upper bound of the settling time can be calculated without initial parameters. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed consensus tracking control approach. A step-by-step procedure for engineers and researchers interested in applications is proposed.

Bogdanov–Takens Bifurcation in a Neutral Delayed Hopfield Neural Network with Bidirectional Connection

In this paper, a neutral Hopfield neural network with bidirectional connection is considered. In the first step, by choosing the connection weights as parameters bifurcation, the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system. In the second step, we studied the zeros of a third degree exponential polynomial in order to make sure that except the double zero root, all the other roots of the characteristic equation have real parts that are negative. Moreover, we find the critical values to guarantee the existence of the Bogdanov–Takens bifurcation. In the third step, the normal form is obtained and its dynamical behaviors are studied after the use of the reduction on the center manifold and the theory of the normal form. Furthermore, for the demonstration of our results, we have given a numerical example.