Event-triggered Synchronization of Uncertain Delayed Generalized RDNNs

This paper investigates the exponential synchronization analysis of master–slave chaotic uncertain delayed generalized reaction-diffusion neural networks (GRDNNs) with event-triggered control scheme. A delay GRDNNs system model for the analysis is constructed by investigating the effect of the network transmission delay. By constructing a novel Lyapunov–Krasovskii functional and using a delay system approach for designing event-triggered controllers and some inequality techniques like Jensen’s inequality, Wirtinger’s inequality and Halanay’s inequality, the criteria are obtained for the event-triggered synchronization analysis and control synthesis of delayed GRDNNs. The synchronization criteria are formulated in terms of linear matrix inequalities. Finally, we conclude that the slave systems synchronize with the master systems. Two examples show the proposed theoretical results are feasible and effective.

A nonlinear version of Halanay's inequality for the uniform convergence to the origin

<p style='text-indent:20px;'>A nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations, with possibly nonconstant time delays, are provided. The relationship with the Razumikhin methodology is shown.</p>

Stability of Stochastic Differential Switching Systems with Time-Delay and Impulsive Effects

This paper studies the stability of hybrid impulsive and switching stochastic neural networks. First, a new type of switching signal is constructed. The stochastic differential switching systems are steerable under the work of the switching signals. Then, using switching Lyapunov function approach, Itô formula, and generalized Halanay’s inequality, some global asymptotical and global exponential stability criteria are derived. These criteria improve the existing results on hybrid systems without noises. An example is given to demonstrate the effectiveness of the results.

Stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima

We study the stability of periodic solutions of the scalar delay differential equation where f(t) is a periodic forcing term and δ,p∈R. We study stability in the first approximation showing that the non-smooth equation (*) can be linearized along some ‘non-singular’ periodic solutions. Then the corresponding variational equation together with the Krasnosel'skij index are used to prove the existence of multiple periodic solutions to (*). Finally, we apply a generalization of Halanay's inequality to establish conditions for global attractivity in equations with maxima.