New globally asymptotical synchronization of chaotic systems under sampled-data controller

Sampled-Data $$H_{\infty }$$ H ∞ Synchronization of Chaotic Lur’e Systems with Time Delay

“…To the end of this section, we derive master-slave synchronization scheme of system (44) without considering disturbance term, which has been studied in [7]. Then, letting ρ = 0, by using Theorem 1 and Corollary 1, we have the following corollary.…”

“…Remark 2 Noted that the term V 6 (t) in L-K functional (21) was newly proposed in Theorem 1 compared with the L-K functional used in [7,9,44]. By introducing the H-dependent term V 6 (t), the constraint conditions of the matrices in the L-K functional have been relaxed.…”

“…Hence, the problem of H ∞ synchronization of chaotic Lur'e system with disturbances has been considered in [10], where they have used continuous delayed feedback control. Recently, robust H ∞ synchronization of chaotic Lur'e system based on the sampled-data controller has been given in [7]. Note that, main aim of the H ∞ control performance is to reduce the effect of external disturbances, that is, disturbance attenuation level is optimized by solving the convex optimization algorithm, which is not given in [7].…”

“…Recently, robust H ∞ synchronization of chaotic Lur'e system based on the sampled-data controller has been given in [7]. Note that, main aim of the H ∞ control performance is to reduce the effect of external disturbances, that is, disturbance attenuation level is optimized by solving the convex optimization algorithm, which is not given in [7]. Moreover, by taking time-varying delays, external disturbances and signal transmission delay into Lur'e system, our sampled-data synchronization problem becomes more and more general than others.…”

“…The problem of H ∞ filtering for time-delay systems has been investigated in [20,22,[30][31][32], whereas stability and stabilization of time-delay systems with disturbances have given in [13,16,19,21]. Recently, the problem of synchronization for identical chaotic Lur'e systems with external disturbance and uncertainties using sampled-data H ∞ controller has been discussed in [7]. However, there are only very few works only having results on H ∞ synchronization problem of Lur'e systems, and thus, there is enough room for extra improvement.…”