Stochastic stabilization of Markov jump quaternion-valued neural network using sampled-data control

Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

“…Substituting equality (18) and inequalities (19) into inequalities (11), and considering inequalities (9), we obtain…”

“…Only a few studies have simultaneously investigated the stability and synchronization of QVNNs. (5) Based on certain important conclusions on stability and synchronization reported in the literature [6,[8][9][10][11][12][13][14][15][16][17][18][19][21][22][23][24][25][27][28][29]31], examples are provided to validate the obtained results. However, no examples are provided to demonstrate the use of QVNNs.…”

“…The delay phenomenon may reduce the convergence rate to equilibria of NNs and even cause considerable damage to the stability of systems. The delay phenomena of NN models have been examined in the literature, including fixed delays [30], variable delays [9][10][11][12][13][21][22][23][24][25][26][31][32][33][34][35][36], infinitely distributed delays [21,33,34,36], and neutral delays [12]. Uncertain interference factors are also unpreventable in NNs.…”

“…Studies [7,[9][10][11]13,14,[19][20][21][23][24][25][26][27] decomposed QVNNs and proposed relevant criteria to ensure system stability or synchronization. However, decomposable quaternion activation functions are rare, and the assumptions associated with decomposable activation functions are strict.…”

“…However, decomposable quaternion activation functions are rare, and the assumptions associated with decomposable activation functions are strict. (3) The scalar Lyapunov function method is the most commonly used method for investigating the stability and synchronization of NNs [6][7][8]10,11,[13][14][15][16][17][18][19]57]. Compared with vector Lyapunov functions, scalar Lyapunov functions are difficult to construct using this method.…”