Unknown inputs observer design for fuzzy systems with application to chaotic system reconstruction

Abstract

This paper deals with the observer design for nonlinear systems in Takagi–Sugeno fuzzy representation. Based on the Lyapunov method and Linear Matrix Inequalities (LMI) formulation, sufficient conditions have been derived for observers design. Unknown inputs can result either from model uncertainty, faults or due to the presence of unknown external excitation. These different results have been widely applied in the field of fault diagnosis and fault tolerance. Based on unknown inputs observer design, secure communication and chaotic system reconstruction problems have been also studied. Examples are given to illustrate a chaotic cryptosystem procedure where the plaintext (message) is encrypted using chaotic signals at the drive system side and the plaintext is retrieved via the designed unknown input observer.