Probability-based event-triggered asynchronous control for fuzzy jump systems (Q6595335)

After obtaining the closed loop equations of a fuzzy jump system with event triggered asynchronous control \N\begin{align*}\N\dot{\zeta}(t) = \sum_{p=1}^\chi\sum_{b=1}^\chi\psi_p\psi_b[A_s^p\zeta(t) +D_s^p\omega(t) + & B_s^p\sum_{\eta=1}^j\tilde{\theta}_t^pK_{m\eta}^b(\zeta(t-\tau^\eta(t))-e(t)) + B_s^p\sum_{\eta=1}^j\bar{\theta}_\eta K_{m\eta}^b(\zeta(t-\tau^\eta(t))-e(t))]\\\N& z(t) = \sum_{p=1}^\chi\sum_{b=1}^\chi\psi_p\psi_bE_s^p\zeta(t)\N\end{align*}\Nthere are proven stochastic stability (for \(\omega(t)\equiv 0\)) and \(H_\infty\) performance for any level \(\gamma>0\) and \(\omega(t)\in L^2(0,\infty)\) under zero initial conditions \N\[\N\displaystyle{E\left\{\int_0^\infty z(t)^Tz(t)dt\right\}\leq\gamma^2E\left\{\int_0^\infty\omega(t)^T \omega(t)dt\right\}}\N\]