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

Abstract

This paper presents a new approach to the output feedback control problem of master-slave synchronization of time-delay chaotic Lur'e systems with sector and slope restricted nonlinearities under communication constraints. The communication constraints involve measurement quantization and signal transmission delay. By constructing an appropriate Lyapunov functional with the idea of a discretized Lyapunov-Krasovskii functional method and utilizing the sector bound of the logarithmic quantizer, a delay-dependent synchronization criterion is derived. The desired synchronization controller can be obtained by solving a set of linear matrix inequalities. Finally, numerical simulations for Chua's circuit are proposed to show the effectiveness of the proposed approach.

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

“…Therefore, error system of the above equation can be written as followṡ (45) and corresponding L-K functional is constructed as…”

Event-Triggered Output Synchronization in Master-Slave Lur’e Systems with Heterogeneous Dimensions

“…It is worth pointing out that the dynamical behavior of chaotic systems is highly sensitive to small changes of any initial conditions, and that the state trajectories in phase space are bounded due to the existence of nonlinearity. Therefore, the problem of chaos synchronization has been widely investigated and a large number of elegant results have been reported in recent years [1,[3][4][5][6][7][8][9][10][11]15,22,[28][29][30][31][32][33][34][35][36][37][38][39][40][41][42].…”

“…Then the issue on synchronization in Lur'e systems has drawn much attention, and many elegant results have been proposed [3][4][5][6][7][8]11,15,[34][35][36][37][38][40][41][42]. For instance, in [34], the finite-time master-slave synchronization and parameter identification have been studied with parameter uncertainties based on adaptive control.…”

“…It is worth noting that time delay is an inherent feature in physical processes and it may lead to instability or significantly deteriorate the system's performance. Thus, many works have considered chaotic synchronization on time-delay Lur'e ones [3][4][5]7,8,11,38,40]. In [4,7,11], with the help of some effective techniques, such as LMI, free-weighting matrix, integral inequality, and convex combination, many elegant results have been proposed with both constant delay and time-varying one included.…”

“…In [4,7,11], with the help of some effective techniques, such as LMI, free-weighting matrix, integral inequality, and convex combination, many elegant results have been proposed with both constant delay and time-varying one included. In particular, the synchronization in [5,8,40] has involved some other factors, such as communication constraints, parameter mismatches, and singular case. Together with impulsive control, the exponential synchronization of nonlinear Lur'e one was studied [3].…”