Proportional-Difference Observer Design for Singular Systems in an LMI Framework

This paper deals with the problem of proportional-difference observer design for singular systems in the discrete-time domain. Several necessary and sufficient conditions for the existence and convergence of the proposed observer are given and proved. Without using any additional transformations, a necessary and sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities. The explicit expression of desired observer is also given. Furthermore, an extension to a class of nonlinear singular systems with Lipschitz constraints is investigated. Finally, a practical example and a numerical one are simulated to illustrate the effectiveness of the proposed approaches.