New improvement results of synchronizing IFS using almost sure stability

The problem of synchronizing chaotic iterated functions system is addressed in this paper. First, a new representation of the observation error system is provided using time scaling approach. Then, based on almost sure stability, a new structure of the observer gains is stated in order to take into account the stochastic jump sequence between one system form to another. The associated design method is established in term of optimization problem under linear matrix inequalities constraints. By computing the top Lyapunov exponent, we show through examples that the proposed approach improve noticeably some existing results.