Synchronization Criteria of Delayed Inertial Neural Networks with Generally Uncertain Transition Rates

In this chapter, we investigate the synchronization problem of inertial neural networks with time-varying delays and generally uncertain transition rates. The second order differential equations are transformed into the first-order differential equations by utilizing the variable transformation method. The Markovian process in the systems is uncertain or partially known due to the delay of data transmission channel or the loss of data information, which is more general and practicable to consider generally Markovian jumping inertial neural networks. The synchronization criteria can be obtained by using the delay-dependent Lyapunov–Krasovskii functionals and higher order polynomial based relaxed inequality. In addition, the desired controllers are obtained by solving a set of LMIs. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results.