This article is concerned with the synchronization control problem for a class of discrete-time dynamical networks with mixed delays and switching topology. The saturation phenomenon of physical actuators is specifically considered in designing feedback controllers. By exploring the mixed-delay-dependent sector conditions in combination with the piecewise Lyapunov-like functional and the average-dwell-time switching, a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances, while the l₂-l∞ performance constraint is satisfied. Furthermore, the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances. Second, by using some congruence transformations, the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities. Then, three convex optimization problems are formulated regarding the disturbance tolerance, the l₂-l∞ performance, and the initial condition set, respectively. Finally, two simulation examples are given to show the effectiveness and merits of the proposed results.

中文翻译：

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执行器饱和下具有切换拓扑的离散时滞动态网络的同步控制。

本文关注的是一类具有混合时滞和切换拓扑的离散时间动态网络的同步控制问题。在设计反馈控制器时，特别要考虑物理执行器的饱和现象。通过探索与混合延迟相关的扇区条件，并结合分段Lyapunov型函数和平均停留时间切换，首先建立了一个充分条件，在该条件下，误差动态的所有轨迹都被限制为允许的初始条件和非零外部扰动，同时满足l2-l∞性能约束。此外，在没有干扰的情况下，对于允许的初始条件，可以确保误差动态的指数稳定性。其次，通过使用一些全等转换，根据一组线性矩阵不等式的可行性，获得了保证存在期望的控制器增益的显式条件。然后，分别针对干扰容忍度，I 2 -I∞性能和初始条件集提出了三个凸优化问题。最后，给出了两个仿真例子来说明所提出结果的有效性和优点。