Robust Dissipativity Analysis of Hopfield-Type Complex-Valued Neural Networks with Time-Varying Delays and Linear Fractional Uncertainties

Abstract

We study the robust dissipativity issue with respect to the Hopfield-type of complex-valued neural network (HTCVNN) models incorporated with time-varying delays and linear fractional uncertainties. To avoid the computational issues in the complex domain, we divide the original complex-valued system into two real-valued systems. We devise an appropriate Lyapunov-Krasovskii functional (LKF) equipped with general integral terms to facilitate the analysis. By exploiting the multiple integral inequality method, the sufficient conditions for the dissipativity of HTCVNN models are obtained via the linear matrix inequalities (LMIs). The MATLAB software package is used to solve the LMIs effectively. We devise a number of numerical models and their empirical results positively ascertain the obtained results.Mathematics 2020, 8, 595 2 of 22 models has been highly focused, resulting in many research studies with comprehensive results [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. On the other hand, it is important to investigate the stability of NN models with the effects of linear fractional uncertainties. Because, when practical systems are modelled, uncertainties of system parameters are often included. From the application point of view, it is important to investigate NN models with linear fractional uncertainties. Several methods for analyzing the dynamical properties of NN models with linear fractional uncertainties have recently been proposed [23,24,39]. By using the Lyapunov function, the robust stability of delayed NN models has been studied with linear fractional uncertainties [23]. In [39], several sufficient conditions have been derived. The study focuses on impulsive NN models, whereby the problem of state feedback synchronization control considering linear fractional uncertainties along with mixed delays has been tackled.An essential property pertaining to dynamical systems is the dissipativity theory. It provides more knowledge than stability. This is because stability analysis is normally strictly related to the phenomenon of energy dissipation or loss. Besides that, the dissipativity theory offers a critical methodology for designing control systems through an input-output representation using system energy-related contemplations. As a result, many publications on the dissipativity analysis of NN models are available in the literature [26][27][28][29][30][31][32][33][34][35][36][37]40]. As an example, a number of new conditions with respect to the (Q, S, R) dissipativity criteria, global exponential dissipativity, and global dissipativity have been developed for a class of CVNN models in [31,37]. In [32], the use of Dini derivative concepts has resulted in novel sufficient conditions for the dissipativity of complex-valued bi-directional associative memory NN models. The dissipativity of discrete-time systems has been studied in [34]. A new concept of dissipativity has been introduced to describe the changes in subsystems and dissipation of energy of the considered system. Most of the existing stu...

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

“…Remark Serval dynamics of neural networks models without fuzzy terms have been examined in previous studies 1,72,73 . In this study, we not only focus on the finite‐time and fixed‐time stabilization of fuzzy neural networks by using the same method proposed in References 1,72,73 but also extend our results to the quaternion domain. As such, the approach proposed in this article is more general and powerful.…”

Offset-free neural network-based nonlinear model predictive controller design using parameter adaptation

“…(v) Solve the optimal control problem posed as Eq. 21 and apply the resulting feedback control law to the process until the next sampling time. (vi) Repeat the procedure from step (i) for the next sampling time, incrementing.…”

“…Cheng et al [16] recently proposed an adaptive neural network control approach to achieve accurate and robust control of nonlinear system with uncertain dynamics in which an adaptive neural network is trained online as the controller and combined with PI controller to achieve asymptotically tracking of setpoint. Rajchakit and coworkers [19][20][21] studied the robust dissipativity and stability of different types of neural networks in the face of parametric uncertainties, time-varying delays and stochastic disturbances. The effectiveness of their method is demonstrated through numerical examples.…”

Stability Analysis Based on Caputo-Type Fractional-Order Quantum Neural Networks

“…The fractional-order neural network was applied in different fields [17][18][19][20][21]. In recent years, the stability of fractional-order neural network system has become a research hotspot [22][23][24][25][26][27][28][29][30][31]. In reference [22], the stability and passivity of a memristor-based fractional-order competitive neural network (MBFOCNN) are analyzed by using Caputo's fractional derivative.…”