Novel Lagrange sense exponential stability criteria for time-delayed stochastic Cohen–Grossberg neural networks with Markovian jump parameters: A graph-theoretic approach

Abstract

This paper concerns the issues of exponential stability in Lagrange sense for a class of stochastic Cohen–Grossberg neural networks (SCGNNs) with Markovian jump and mixed time delay effects. A systematic approach of constructing a global Lyapunov function for SCGNNs with mixed time delays and Markovian jumping is provided by applying the association of Lyapunov method and graph theory results. Moreover, by using some inequality techniques in Lyapunov-type and coefficient-type theorems we attain two kinds of sufficient conditions to ensure the global exponential stability (GES) through Lagrange sense for the addressed SCGNNs. Ultimately, some examples with numerical simulations are given to demonstrate the effectiveness of the acquired result.

Parametric design to reduced-order functional observer for linear time-varying systems

“…Then, equation ( 33) indicates (35). Combining equations ( 25)-( 29) yields (31). Particular, the matrix M(t) is determined by (29), and it is solvable if and only if rank T1 (t)…”

“…The use of some mathematical methods, including matrix equations, nonlinear equations play a vital role in the establishment and application of control theory and system models. [28][29][30][31] Zhou and Duan, 32 Duan, 33 Gu and Zhang, 34,35 Gu et al 36,37 studied the fully parameterized solution of homogeneous generalized Sylvester equations (GSEs), and its application in typical control problems such as characteristic structure configuration and observer design, which laid a solid theoretical foundation for control system design. Based on the results of the fully parameterized solution of GSEs proposed in Zhou and Duan, 32 this study investigates the problem of state reconstruction for LTV models.…”

“…Step 5.Complete the observer construction Compute gain matrices according to equation (31) to complete the construction of reduced-order functional observer.…”

Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory

“…By the locally Lipschitz character of model ( 2)'s right-side function and the equivalent model (3), positive solutions' local existence is obvious. Now, we will construct a compact subset to prove the positive solutions' global existence [14][15][16][17][18].…”

H∞ synchronization of Markov jump neural networks with MPDT switching transition probabilities under DoS attacks

“…In order to facilitate the transmission between signals, network transmission can be adopted. However, when a large amount of data is transmitted, limited communication resources may lead to the emergence of network induced phenomena, such as packet loss, network delay, and network security [26][27][28][29][30]. Among these factors, the packet loss and network delay have been widely studied for synchronous control problem of MJNNs [31,32], while network security is easily ignored.…”