Novel LMI-based adaptive boundary synchronisation of fractional-order fuzzy reaction–diffusion BAM neural networks with leakage delay

ABSTRACT

The boundary synchronisation problem of fractional-order fuzzy reaction–diffusion BAM neural networks with leakage delay is investigated. A novel adaptive boundary controller, Neumann boundary condition, and fuzzy feedback MIN and MAX templates of nonlinear dynamic fuzzy modelling are employed. We developed adaptive sufficient criteria to check the asymptotic stability of error dynamical system by using suitable Lyapunov functional, Wirtinger's inequality and LMI method, which guarantee the drive-response dynamical systems achieve the synchronisation. Meanwhile, two different controllers, adaptive full-domain and boundary controllers are developed. At last, numerical simulations are presented to demonstrate the feasibility of the theoretical results.

KEYWORDS:

• Fuzzy BAM neural networks
• reaction–diffusion terms
• leakage delay
• adaptive boundary control
• linear matrix inequality
• synchronisation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

We thank the financial support from the National Research Council of Thailand (Talented Mid-Career Researchers) Grant Number N42A650250.