An improved condition for master–slave synchronization of Lur'e systems with time delay

New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control

“…While the synchronization can be manifested until the maximum delay h = 0.28 in [10], h = 0.213 in [21] and [7], h = 0.222 in [20], h > 0.25 in [8] respectively. This implies that our criterion is less conservative than that in [3] and [7,8,10,20,21]. e (t) = (A + ∆A (t)) e (t) + (B + ∆B (t)) η (Ce (t) , y (t)) − MHe (t − h (t)) , It is clear that the state trajectories approach to zero asymptotically.…”

“…Liao and Chen [11] and Cao et al [1] further generalized and improved the results in [21] and employed model transformation, which leads to some conservative synchronization criteria for inducing additional terms. Shortly, some new approaches are employed to avoid using model transformation and derive much less conservative synchronization conditions, for example, Xiang et al [20], He et al [8] used integral inequality [22] in the derivative of Lyapunov functional respectively, and it turned out that the permissible delay threshold can be fairly enlarged both in theory and in numerical experiment. However, with the development of the time, many methods to reduce the conservatism have been produced and applied in many other fields such as the integral inequality techniques used in neural network [19], and achieved good results.…”

Exponential synchronization of chaotic Lur’e systems with delayed feedback control

“…More recently, the linear matrix inequality (LMI) technique has been applied to discuss the master-slave synchronization problem for chaotic systems, which can be readily facilitated by resorting to some available numerical packages [19,20]. In [21][22][23][24], several sufficient conditions in terms of LMIs were presented to ensure that the controlled slave system can synchronize with the master system. The authors in [25] studied the master-slave synchronization problem by introducing some free-weighting matrices.…”

Synchronization for Time-Delay Lur’e Systems with Sector and Slope Restricted Nonlinearities Under Communication Constraints

“…systems can represent a class of nonlinear systems, such as Chua's circuit, n-scroll attractors, and hyperchaotic attractors, the problem of stabilization and synchronization for chaotic Lur'e systems has been investigated by many researchers [1,4,15,18,19,21,22,26,27,33,34]. In particular, with consideration of the propagation delay, frequently encountered in the remote master-slave synchronization scheme, some delay-dependent criteria for the design of delayed feedback controllers were proposed to achieve the master-slave synchronization of Lur'e systems [1,15,18,19,27,34].…”

“…In particular, with consideration of the propagation delay, frequently encountered in the remote master-slave synchronization scheme, some delay-dependent criteria for the design of delayed feedback controllers were proposed to achieve the master-slave synchronization of Lur'e systems [1,15,18,19,27,34].…”