Observer-based exact synchronization of ideal and mismatched chaotic systems

Homogeneous finite time observer for nonlinear systems with linearizable error dynamics

“…Several chaotic systems, as the three-dimensional GenesioTesi system [8], the Lur'e-like system or the Duffing equation [13], belong to the class of systems (4)(5). In this section, the Chua's system is considered to show the effectiveness of the proposed approach.…”

“…Thus, the Chua's circuit is in a similar form as (4)(5). In [7] and [13], the authors designed a step-by-step sliding mode observers to perform finite time synchronization of this chaotic system. However, the estimation is based on a step-by-step procedure using successive filtering values of the so-called equivalent output injections obtained from recursive first order sliding mode observers.…”

Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

“…A variety of observer-based approaches have been proposed for the synchronization of chaotic systems, which include the exponential polynomial observer [16], sliding observer [17], adaptive sliding observer [18], higher order sliding mode observer [19], fuzzy disturbance observer [20], Thau observer [21]. Synchronization of fractional-order chaotic systems was studied by Deng and Li [22] who carried out synchronization in case of the fractional Lu system.…”

“…Among the array of methods proposed for synchronization of chaotic dynamics, observer based methods [16][17][18][19][20][21] are the focal point of interest in the field of integer chaos synchronization, but a lack of observer schemes impedes designing and stability analysis under in fractional systems. This is why we developed a sliding observer scheme for synchronizing fractional-order chaotic dynamics.…”

“…This is why we developed a sliding observer scheme for synchronizing fractional-order chaotic dynamics. The observer scheme designed in this manuscript is a generalization of the work proposed for integer-order chaotic dynamics [17]. Stability analysis of the closedloop fractional-order system is proved by a classical Lyapunov method.…”