Sobolev Norms-Based State Estimation and Input Recovery for a Class of Nonlinear Systems. Design and Experimental Results

In this paper, we address the problem of state estimation and input recovery for a class of nonlinear systems in the presence of disturbances in both the state and output equations. Indeed one of the main difficulties, that arise when input recovery is considered, is how to cope with the problem of disturbance's derivative for the filter design. Our contribution lies in the use of Sobolev norms to develop a simple and useful observer. We provide first the state filtering and input recovery equations. After, based on the Lyapunov stability theory and some robustness criteria, new sufficient synthesis conditions are given in terms of linear matrix inequalities (LMIs). To show performances of the proposed method, we considered the problem of simultaneous synchronization and decryption in chaotic communication systems with some experimental results.