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.