Impulsive observer with predetermined finite convergence time for synchronization of fractional-order chaotic systems based on Takagi–Sugeno fuzzy model

This paper is devoted to the problem of observer design for synchronization of nonlinear fractional-order chaotic systems described by the Takagi–Sugeno fuzzy model. We propose a new method of designing an observer that converges in finite time. The novelty of the proposed observer compared to those developed in the literature is that the estimated state exactly converges to the true state in a finite time which can be chosen beforehand. This is made possible by updating the estimated state at a defined time instant. The abrupt update shows up an impulsive behavior of the observer’s dynamics. Two cases are considered. In the first case, the system is not affected by an unknown input. The second case considers the system subjected to the action of an unknown input. Finite-time convergence of the two proposed observers for both cases is established using linear matrix inequality formulation. Simulation results on the synchronization of fractional-order chaotic systems clearly illustrate the impulsive behavior of the proposed observer and the predefined finite-time synchronization. The advantage of predefined finite-time synchronization is highlighted by the ability of recovering an encrypted message without loss of information in a fractional-order chaos-based secure communication application.