Synchronization Control for Discrete-Time-Delayed Dynamical Networks With Switching Topology Under Actuator Saturations

• Published in: IEEE transaction on neural networks and learning systems Vol. 32; no. 5; pp. 2040 - 2053
• Main Authors: Chen, Yonggang, Wang, Zidong, Hu, Jun, Han, Qing-Long
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.05.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuator saturations; Actuators; Convexity; Delays; discrete-time networks; Disturbances; Dynamic stability; dynamical networks; Feedback control; Initial conditions; Linear matrix inequalities; Mathematical analysis; mixed delays; Network topologies; Network topology; Optimization; Switches; Switching; switching topology; Synchronism; Synchronization; synchronization control; Time synchronization; Topology
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2020.2996094

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 <inline-formula> <tex-math notation="LaTeX">l_{2} </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">l_\infty </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">l_{2} </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">l_\infty </tex-math></inline-formula> performance, and the initial condition set, respectively. Finally, two simulation examples are given to show the effectiveness and merits of the proposed results.