Reduced-order fractional integral observer for synchronisation and anti-synchronisation of fractional-order chaotic systems

In this study, the problems of synchronisation and anti-synchronisation are solved for commensurate and incommensurate fractional chaotic systems. A reduced-order fractional integral observer is proposed for fractional systems satisfying a fractional algebraic observability condition, which is shown to be Mittag-Leffler stable. This observer is used as a slave system, whose states are synchronised with the states of the chaotic system, which acts as a master. The observer uses a reduced set of measurable signals from the master system, solving the anti-synchronisation problem as a straightforward extension of the synchronisation one. Numerical simulations on the fractional Lorenz and Rossler systems assess the performance of the proposed methodology.