title: Convergence and attractivity of memristor-based cellular neural networks with time delays.
abstract: This paper presents theoretical results on the convergence and attractivity of memristor-based cellular neural networks (MCNNs) with time delays. Based on a realistic memristor model, an MCNN is modeled using a differential inclusion. The essential boundedness of its global solutions is proven. The state of MCNNs is further proven to be convergent to a critical-point set located in saturated region of the activation function, when the initial state locates in a saturated region. It is shown that the state convergence time period is finite and can be quantitatively estimated using given parameters. Furthermore, the positive invariance and attractivity of state in non-saturated regions are also proven. The simulation results of several numerical examples are provided to substantiate the results.
authors.affiliation: School of Control Science and Engineering, Dalian University of Technology, Dalian 116023, China; Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, 264209, China. Electronic address: qinsitian@163.com.
authors.forename: Sitian
authors.initials: S
authors.lastname: Qin
authors.affiliation: Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong; School of Control Science and Engineering, Dalian University of Technology, Dalian 116023, China. Electronic address: jwang@mae.cuhk.edu.hk.
authors.forename: Jun
authors.initials: J
authors.lastname: Wang
authors.affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China. Electronic address: xiaopingxue@263.net.
authors.forename: Xiaoping
authors.initials: X
authors.lastname: Xue
mesh_terms: D000465:Algorithms; D016571:Neural Networks, Computer; D013997:Time Factors
keywords: Attractivity; Cellular neural networks; Finite-time convergence; Memristor; Positive invariance