This paper treats the estimation of the state of a nonlinear system with unknown input. The nonlinear system is described by a multimodel with unknown function of activation but depending only on the state. The method of design of the multiobserver is described by using the second method of Lyapunov and their candidate functions. The sufficient obtained stability conditions are expressed in terms of Linear Matrix Inequalities (LMI) and are obtained first using the Lyapunov quadratic functions and secondly by using Lyapunov polyquadratic functions. This latter technique seems to be less conservative and less constraining than the first. Illustrative examples are presented in this paper.