Improved synchronization criteria of Lur’e systems under sampled-data control

Abstract

In this paper, we address the issue of $$\mathcal {H}_{\infty }$$ synchronization for two identical chaotic systems with time-varying delays and uncertainties under sampled-data control. By developing some new terms, an improved piecewise Lyapunov–Krasovskii functional (LKF) is constructed to take full advantage of characteristic about real sampling and nonlinear function vector. Furthermore, some relaxed matrices constructed in LKF are not necessarily positive definite. By using the LKF and free-matrix-based integral inequality, some sufficient criteria can be obtained to ensure the stability of error systems and reduce the influence of external disturbances with an $$\mathcal {H}_{\infty }$$ norm bound. The sampled-data controller can be synthesized by solving a group of linear matrix inequalities with the maximal sampling interval. Finally, the numerical examples are considered and analyzed by the proposed approach so as to show the benefit and the superiority of the proposed approach.