Finite-Time Synchronization Control for Markovian Jump Memristive Neural Networks with Reaction-Diffusion Terms

Abstract

This chapter investigates the issue of finite-time synchronization for a class of memristive neural networks, where the reaction-diffusion items and Markovian jump parameters are both considered. Specifically, the drive and response systems proposed in this chapter follow the inconsistent Markov chains, which might be in accordance with realistic applications better. Meanwhile, a novel discontinuous controller is designed, so that the difficulty in deriving the synchronization criterion of time-space related second-order differential systems (SODSs) can be solved. In the process of dealing with the derivative of Lyapunov–Krasovskii functional (LKF), a canonical Bessel–Legendre inequality (BLI), which converts the limited interval required in traditional BLI to a general one, is employed. The main work is reflected as follows: first, the original SODSs is converted into a first-order differential system by employing a suitable variable substitution and then the error system in a compact first-order differential form is established; second, a less conservative criterion of finite-time synchronization is obtained by constructing a new LKF and utilizing the canonical BLI and free-weighting matrix methods. Ultimately, a numerical example and an application study are exploited to illustrate the feasibility and practicability of this chapter, thus the acquired theoretical results can be well supported.