Unknown Input Observer Design for a Class of Linear Descriptor Systems

¹ Laboratory of High Energy Physics and Condensed Matter, Faculty of Science, Hassan II University of Casablanca. B.P 5366, Maarif, Casablanca, Morocco.
² ECPI, Department of Electrical Engineering, ENSEM, Hassan II University of Casablanca. B.P 8118, Oasis, Casablanca, Morocco.

^* e-mail: karim.bouassem@gmail.com
^** e-mail: a.elassoudi@ensem.ac.ma
^*** e-mail: jalal.soulami@gmail.com
^**** e-mail: h.elyaagoubi@ensem.ac.ma

Abstract

This paper addresses the problem of unknown inputs observer (UIO) design for a class of linear descriptor systems. The unknown inputs affect both state and output of the system. The basic idea of the proposed approach is based on the separation between dynamic and static relations in the descriptor model. Firstly, the method used to separate the differential part from the algebraic part is developed. Secondly, an observer design permitting the simultaneous estimation of the system state and the unknown inputs is proposed. The developed approach for the observer design is based on the synthesis of an augmented model which regroups the differential variables and unknown inputs. The exponential stability of the estimation error is studied using the Lyapunov theory and the stability condition is given in term of linear matrix inequality (LMI). Finally, to illustrate the efficiency of the proposed methodology, a heat exchanger pilot model is considered.