Dissipativity and passivity analysis for discrete‐time complex‐valued neural networks with leakage delay and probabilistic time‐varying delays

• Published in: International journal of adaptive control and signal processing Vol. 31; no. 6; pp. 876 - 902
• Main Authors: Ramasamy, S., Nagamani, G.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.06.2017
• Subjects: complex‐valued neural networks (CVNNs); Delay; Dissipation; dissipativity; Economic models; Leakage; Linear matrix inequalities; linear matrix inequality; Lyapunov–Krasovskii functional (LKF); Mathematical analysis; Matrix methods; Neural networks; Passivity; Probabilistic methods; probabilistic time‐varying delays; Probability theory
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.2736

Summary In this paper, the problem of dissipativity and passivity analysis is investigated for discrete‐time complex‐valued neural networks with time‐varying delays. Both leakage and discrete time‐varying delays have been considered. By constructing a suitable Lyapunov–Krasovskii functional and by using discretized Jensen's inequality approach, sufficient conditions have been established to guarantee the (Q,S,R) − γ dissipativity and passivity of the addressed discrete‐time complex‐valued neural networks. These conditions are derived in terms of complex‐valued linear matrix inequalities (LMIs), which can be checked numerically using Yet Another LMI Parser toolbox in Matrix Laboratory. Finally, three numerical examples are established to illustrate the effectiveness of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.