Improved Synchronization Analysis via Looped-Lyapunov for Stochastic Markovian Jump Neural Networks

The synchronization problem of delay-dependent stochastic Markovian jump neural networks (SMJNNs) is examined in this short note. A sampled data controller is designed for this synchronization problem, which synchronizes the uncontrolled and controlled SMJNNs. A looped Lyapunov functional is presented that contains the sampling information, and it is not required to be zero at $t_{k}$ and is not required to be continuous. Instead, it must satisfy the condition that $V(t_{k}^{-}) \geq 0$ and $V(t_{k})=0$ or $V(t_{k}^{-}) = 0$ and $V(t_{k}) \leq 0$ . To ensure stochastic stability in the mean square of the error system, sufficient conditions are obtained by using the It $\hat {\mathrm{ o}}$ 's formula, integral inequalities, which are given as linear matrix inequalities (LMIs). The proposed results are validated by comparing them with existing results in numerical examples.