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This study examines the leader-following consensus problem of a class of second-order nonlinear multi-agent systems, where the velocity information is supposed to be unmeasurable. Under the setting, this paper presents a novel aperiodically intermittent output feedback control protocol such that all followers reach consensus with the leader, in which a distributed state observer is built for each follower to observe the velocity state. Based on the Lyapunov stability theory and some matrix analysis techniques, a couple of sufficient conditions for the leader-following consensus of the nonlinear multi-agent system under study are obtained even though the velocity state is unavailable. Finally, the effectiveness of the theoretical results is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

Drawing on Vygotsky’s Sociocultural Theory (SCT) and the theory of Instructional Conversation (IC), this study explores the development of L2 learners’ understanding of the second conditional during an IC in an online teaching video made by Macmillan Learning Teaching Education. During the IC, the instructor leads students toward a conceptual understanding of the second conditional by providing appropriate mediation sensitive to the class’s zone of proximal development (ZPD). The transcripts of the IC are analyzed with regard to the amount and type(s) of instructional mediation and the development opportunities created in this type of collaborative interaction. The analysis demonstrates the conceptual and linguistic development among the students in terms of the second conditional and shows the value of IC in creating a ZPD to promote L2 conceptual and linguistic development. In addition, this study raises the awareness of the value of online teaching videos in Sociocultural Theory and teacher education.