Unknown input observer for 2-D Fornasini-Marchesini system using descriptor system approach

This paper considers the problem of estimating the state and unknown input simultaneously for 2-D Fornasini-Marchesini system with unknown input in both state and measurement equations. The problem is solved by using descriptor system approach and then an asymptotically convergent observer was designed. Two cases, the gain matrix for the unknown input in measurement equation is not and/or is of full column rank, have been discussed. For these two cases, the corresponding sufficient and necessary condition and sufficient condition for the existence of the asymptotical observers are presented and proved in terms of rank condition, respectively. A numerical example is provided to illustrate the convergence properties of the observers and the effectiveness of the proposed method.