$$\mathcal{H}_{\infty }$$ weight learning of dynamic neural networks with delay and reaction–diffusion

Weight learning for ℋ∞$$ {\mathscr{H}}_{\infty } $$ stabilization of uncertain switched neural networks with external disturbance and reaction‐diffusion

“…Remark It is noteworthy that, by denoting 39 $$$$ \mathscr{H}(t)=\frac{\int_0^t{\int}_{\Omega}{\nu}^T\left(s,\sigma \right) S\nu \left(s,\sigma \right) ds\kern.15em d\sigma}{\int_0^t{\int}_{\Omega}{d}^T\left(s,\sigma \right)d\left(s,\sigma \right) ds\kern.15em d\sigma}, $$$$ one can rewrite () as $$$ \mathscr{H}\left(\infty \right)\le {\gamma}^2 $$$. When $$$ \nu \left(s,t\right) $$$ and $$$ d\left(s,t\right) $$$ are independent of the space value s, () becomes $$$$ {\int}_0^{\infty }{\nu}^T(t) S\nu (t) dt\le {\gamma}^2{\int}_0^{\infty }{d}^T(t)d(t) dt, $$$$ and the concept of $$$ {\mathscr{H}}_{\infty } $$$ stability corresponds to that discussed in References 40‐42.…”