In this brief, we consider the consensus problem of hybrid multiagent systems. First, the hybrid multiagent system is proposed, which is composed of continuous-time and discrete-time dynamic agents. Then, three kinds of consensus protocols are presented for the hybrid multiagent system. The analysis tool developed in this brief is based on the matrix theory and graph theory. With different restrictions of the sampling period, some necessary and sufficient conditions are established for solving the consensus of the hybrid multiagent system. The consensus states are also obtained under different protocols. Finally, simulation examples are provided to demonstrate the effectiveness of our theoretical results.

La théorie et la recherche concernant les croyances (LOC) et les perceptions du contrôle suggèrent que les Asiatiques tendent à obtenir des scores plus bas et à être plus passifs que les Américains, mais ces travaux ont été menés à l'aide de concepts et d'échelles développés principalement aux USA qui certifient une primauté du contrôle interne (ex: en changeant l'environnement pour l'adapter à soi). Une équipe de recherche internationale a étendu la notion de croyance dans le contrôle en développant des échelles qui permettent de reconsidérer la notion en faisant état de croyances secondaires dans le contrôle (ex: en adaptant le soi à l'environnement) et de faire état d'un concept nouveau de croyances socio-instrumentales (ex: le contrôle par les relations interpersonelles) qui permettent de rendre compte de manière plus pertinente des croyances en un contrôle dans les cultures collectivistes. Nous nous attendions à ce que, par l'utilisation d'échelles culturellement appropriées, les Américains n'obtiennent pas une croyance en un contrôle plus importante que les Asiatiques. Les hypothèses ont été partiellement confirmées en ce que les Américains se sont montrés comme obtenant un contrôle plus bas que les Chinois (de Hong Kong et de RP de Chine) sur ces échelles. Il est suggéré que voir les Asiatiques comme évitant passivement le contrôle au travail peut être incorrect et dû aux insuffisances de contrôle socio-instrumental.Research and theory concerning beliefs (locus of control) and perceptions of control suggest that Asians tend to be lower and more passive than Americans, but this work has been conducted mainly with US-developed constructs and scales that assess primary control (i.e. changing the environment to adapt to the self ). An international research team expanded the notion of control beliefs by developing scales to assess secondary control beliefs (i.e. adapting the self to the environment) and the new construct of socioinstrumental control beliefs (i.e. control via interpersonal relationships), both of which were thought to better fit the control beliefs of collectivist cultures than Westerndeveloped control scales. We expected that, when culturally appropriate scales were employed, Americans would not show higher control beliefs than Asians. Hypotheses were partially confirmed that Americans would be lower than Chinese (Hong Kong and PR China) on these new scales. It is suggested that views of Asians as passive avoiders of control at work may be incorrect and due to the overlooking of socioinstrumental control.

Summary This paper considers a consensus problem for hybrid multiagent systems, which comprise two groups of agents: a group of continuous‐time dynamic agents and a group of discrete‐time dynamic agents. Firstly, a game‐theoretic approach is adopted to model the interactions between the two groups of agents. To achieve consensus for the considered hybrid multiagent systems, the cost functions are designed. Moreover, it is shown that the designed game admits a unique Nash equilibrium. Secondly, sufficient/necessary conditions of solving consensus are established. Thirdly, we find that the convergence speed of the system depends on the game. By the mechanism design of the game, the convergence speed is increased. Finally, simulation examples are given to validate the effectiveness of the theoretical results.

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