Quantized $H_{\infty}$ Consensus of Multiagent Systems With Quantization Mismatch Under Switching Weighted Topologies

Abstract

This paper investigates the distributed quantized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus problems for general linear and Lipschitz nonlinear multiagent systems with input quantization mismatch and external disturbances under switching weighted undirected or balanced directed topologies. The designed distributed quantized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus protocol can be divided into two parts which are linear and nonlinear parts. The linear part plays a role in achieving satisfactory performance against interval-bounded model uncertainties, external disturbances, and unknown initial states. The nonlinear part eliminates the effect of input quantization. It should be mentioned that complete consensus instead of practical consensus can be achieved in the presence of uniform quantization. In addition, instead of requiring the coupling strength among neighboring agents to be larger than a threshold value as in previous literature, the coupling strength in this paper can be determined by solving some linear matrix inequalities. Sufficient conditions for the existence of the proposed control strategy are also obtained by using the LMI technique. Finally, two numerical examples are presented to show the effectiveness and advantages of the proposed consensus strategy.