This　paper　considers　the　problem　of　robust　analysis　for　the　distributed　network　system,　whose　subsystem　is　Lure　system,　i.e.　the　kind　of　nonlinear　systems　with　sector　constraint　function.　Based　on　the　stability　condition　for　single　Lure　system,　and　considering　the　characteristic　of　the　distributed　network　systems,　using　hybrid　Lyapunov　equation,　the　methods　of　robust　analysis　for　the　uncertain　distributed　network　systems　are　given,　and　the　corresponding　linear　matrix　inequalities　(LMIs).