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This paper focuses on the average consensus problem of first-order and second-order continuous-time multiagent systems with logarithmic quantized information transmission. The balanced and strongly connected digraphs are utilized to characterize the interaction topologies between agents. Based on the state estimation, distributed state updating mechanisms are introduced for every agent such that all agents' states achieve average consensus asymptotically. By means of differential inclusion theory, we discuss the existence and convergence property of the Krasovskii solutions to the closed-loop system models. By designing the proper control gain parameters and quantizer accuracy, two sufficient conditions are established to guarantee the achievement of average consensus. Finally, two numerical simulations are provided to illustrate the effectiveness of theoretical results. INTRODUCTIONOver the past decade, the distributed coordination control of multiple agents has received compelling attention from various scientific communities, because of its broad applications in many fields such as formation of mobile vehicles [1,2], cooperative control of robots [3,4], flocking behavior [5], data fusion of sensory networks [6], and so on.A typical and widely investigated problem in distributed control is the consensus problem, which aims at driving all agents to reach agreement upon some quantities of interest by designing the distributed algorithm for each agent. The consensus problem of multi-agent systems (MASs) under various situations, such as, continuous-time (CT) or discrete-time (DT) dynamics, fixed or dynamic communication topologies, with or without time delays, and so on, has been studied in many previous literatures [7][8][9][10][11][12][13].Most of existing results on consensus problem are derived under the assumption that accurate state information of agents can be transmitted and received. Unfortunately, this is usually inconsistent with the facts. With the rapid development of computer and network, information is usually transmitted and received in digital signals through networks. Because of the limitation of network bandwidth, the original precise data need to be truncated or quantized. Quantization can reduce the quantity of data transmission, whereas it can increase the complexity of system control. In view of the widespread applications of quantization in real physical systems, many researchers in control community have begun to investigate the quantization effects on distributed control of 3346 Y. WU AND L. WANG multiple vehicles. With respect to the quantized consensus problem, there are four types of commonly used quantizers, namely, uniform quantizer (UQ) [14][15][16][17][18][19][20], probabilistic quantizer [16,21], dynamic quantizer (DQ) [22,23] and logarithmic quantizer (LQ) [24][25][26][27][28].Based on the aforementioned four types of quantizers, subsequently, we present some existing results on quantized consensus. The concept of 'quantized consensus' was first introduced in [14], where a quanti...

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This work aims to study the gas phase hydrodynamics in a stirred tank with a surface‐aerated long‐short blades agitator by the Eulerian–Eulerian approach coupled with population balance model. Predicted local gas holdup and bubble size distribution agree well with those measured by a conductivity probe technique. The predictions demonstrate that the pressure depression in the center is the main driving force for gas suction and the downward flow carries the bubbles down to redistribute in the whole tank. The gas phase has higher gas holdup with large bubble size in the upper part and lower gas holdup but with small bubble size in the lower part of the tank. The predicted liquid‐phase mass transfer coefficients agree well with our previous experimental results and just depend on the power consumption per unit volume when the aspect ratio of the liquid height to the tank diameter varies from 1.1 to 2.0.

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