Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays

In this paper, the problem of dissipativity analysis for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is investigated extensively. Dissipativity analysis is an important concept in control system theory and its applications. The analysis in the paper employ results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By using the framework of Filippov solution, differential inclusion theory, an appropriate Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique, several new sufficient conditions for global dissipativity, global exponential dissipativity and strictly (Q,S,R)(Q,S,R)-dissipativity are derived in the form of complex-valued as well as real-valued LMIs. Both real and complex-valued LMIs guarantee feasibility results for addressed MCVNNs. These LMIs can be solved by using standard available numerical packages. Moreover, the global attractive sets which are positive invariant are obtained. Finally, three numerical examples are established to illustrate the effectiveness of the proposed theoretical results.