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

Abstract

This paper studies the problem of master-slave synchronization for uncertain Lur'e system via time-varying delayed feedback control. It proves a new inequality involving double integrals, which can reduce the conservatism of the known Jensen's like inequalities according to our analysis. By employing this new inequality and a new class of novel mode-dependent augmented Lyapunov-Krasovskii functional (LKF), it establishes some novel synchronization criteria, where the controller gain can be achieved by solving a set of linear matrix inequalities (LMIs). Two examples with numerical simulations are given to illustrate the feasibility and the superiority of our methods.

Improvement master-slave robustly synchronous criteria of uncertain chaotic Lur'e systems via an augmented Lyapunov-Krasovskii functional

“…The MADUBs h can be calculated by solving the LMIs ( 8)-( 9) and ( 25) in Theorem 2 via Matlab LMI-TOOL box. The corresponding results and those compared with some literatures [16][17][18] are listed in Table 3, which shows that the theorem 2 proposed in this paper is less conservative than those given in some recent literatures. However, the number of decision variables in LMIs ( 8)-( 9) and ( 25) is more than those given in some recent literatures, which shows the conservatism of synchronization stability criterion is reduced at the cost of increasing solution complexity.…”

“…For this example, our results of MADUBs h are listed in compared with some existing literature [16][17][18]. The detail analysis and discussions are summarized as follows.…”

“…• Secondly, consider µ 1 ̸ = 0, which is ignored in [16][17][18]. The corresponding MADUBs h are listed in Table 4 for different µ 1 and µ 2 .…”

“…Nowadays, many methods are used to study chaos Lur'e systems with time delays. The most popular method is the so-called input delay method, where the system is converted to a system with time-varying input delay caused by a zero-order hold, such as, sampled-data control [5,6], delayed state-feedback control [7][8][9][10][11][12][13][14][15][16][17], etc.. The synchronization criterion is mainly derived from Lyapunov stability theory, which is a sufficient condition and inevitably conservative.…”

Improvement master–slave robustly synchronous criteria of uncertain chaotic Lur’e systems via an augmented Lyapunov–Krasovskii functional

“…Nowadays, many methods are used to study chaos Lur’e systems with time delays. The most popular method is the so-called input delay method, where the system is converted to a system with time-varying input delay caused by a zero-order hold, such as sampled-data control (Hai, 2022) and delayed state-feedback control (Ge et al, 2014; Lenka and Bora, 2023; Li et al, 2011; Min et al, 2022; Shi et al, 2016; Wang et al, 2017; Zhang et al, 2019). The synchronization criterion is mainly derived from Lyapunov stability theory, which is a sufficient condition and inevitably conservative.…”