Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems

This paper is concerned with the design of the novel observer that synchronizes with the generalized Lorenz chaotic systems. A simple reduced-order observer scheme is proposed by including extra terms. The boundedness of the state variables in the original system is not necessary for the observer design. The prior knowledge on the derivative signal of the system output is not required. It is also shown that by adopting Lyapunov method and choosing appropriate design parameters, the synchronization (observation) errors can converge to zero exponentially. Finally, numerical examples are provided to illustrate the validity of the theoretical result.