Fixed-time synchronization for quaternion-valued memristor-based neural networks with mixed delays

Synchronization Analysis for Quaternion-Valued Delayed Neural Networks with Impulse and Inertia via a Direct Technique

“…In [17,[21][22][23], the synchronization of QV-NNs has been discussed, in which the models of QV-NNs were rewritten as real-valued or complex-valued submodels via the separation method, and then each submodel was controlled to achieve synchronization. Different from the analysis method of separation before control, two types of quaternion-valued control schemes are directly proposed for the response QV-NNs in this article, and convergence analysis is achieved without using the separation technique.…”

“…Meanwhile, delay is inevitable because of network parameter fluctuations during hardware operation, the limited speed of transmission of signals and the switching of amplifiers. Currently, various QV-NN models with different types of delays have been investigated, including mixed delay [17], leakage delay [18], proportional delay [9,19] and time-varying delay [20].…”

“…Note that the main method adopted in the above results is the separation technique; that is, the original QV-NNs are divided into two CV-NNs or four RV-NNs [17,[21][22][23]. This method of separation is feasible, but it has some inevitable weaknesses.…”

“…In addition, a convergence result on piecewise differentiable functions is derived, which is a generalization of the Barbalat lemma [48] and provides a vital tool for the convergence analysis of impulsive models. (2) Under constant gain-based control and adaptive gain-based control, two kinds of quaternion-valued control schemes are directly developed for the response QV-INNs, which are distinct from the control designs on the reduced-order systems of inertial NNs in [31,32] and the control strategies on subsystems obtained by separation used in [17,[21][22][23].…”

“…(3) Without using the separation technique and reduced-order transformation proposed in [17,[21][22][23]31,32], a direct analysis method is developed to discuss the synchronization of QV-INNs. In particular, some Lyapunov functionals, composed of the state variables and their derivatives, are directly constructed for the QV-INNs and some synchronization conditions represented by matrix inequalities are obtained based on quaternion theory and the established convergence result on piecewise differentiable functions.…”