Abstract
This research paper deals with the passivity and synchronization problem of fractional-order memristor-based competitive neural networks (FOMBCNNs) for the first time. Since the FOMBCNNs’ parameters are state-dependent, FOMBCNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, the conventional robust control scheme cannot guarantee the synchronization of FOMBCNNs. Under the framework of the Filippov solution, the drive and response FOMBCNNs are first transformed into systems with interval parameters. Then, the new sufficient criteria are obtained by linear matrix inequalities (LMIs) to ensure the passivity in finite-time criteria for FOMBCNNs with mismatched switching jumps. Further, a feedback control law is designed to ensure the finite-time synchronization of FOMBCNNs. Finally, three numerical cases are given to illustrate the usefulness of our passivity and synchronization results.
Highlights
In recent years, the research on competitive-type neural networks (CNNs) has attracted expanding consideration from mathematicians, engineers, physicists and scholars
Motivated by the aforementioned issues, this paper aims at analyzing the finite-time passivity and finite-time synchronization criterion of FOMBCNNs
FOMBCNNs (72) and (73) are synchronized in finite time based on Theorem 2, and are displayed in Figures 9–11; we get an upper bound of the settling time t ≤ 2.2871
Summary
The research on competitive-type neural networks (CNNs) has attracted expanding consideration from mathematicians, engineers, physicists and scholars. There are two forms of state variables: short-term memory and long-term memory. They make a good application background in convex optimization, cybernetics, image recognition and associative memory. Have been obtained, but these results are mainly discussed in integer-order cases. There are few results focused on CNNs with fractional-order cases, see [9,10,11,12,13]. As the fourth circuit component along with resistor, capacitor and inductor, memristor was firstly postulated by Professor Chua in 1971 [14].
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