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Molybdenum disulfide bilayers with well-defined interlayer twist angle were constructed by stacking single-crystal monolayers. Varying interlayer twist angle results in strong tuning of the indirect optical transition energy and second-harmonic generation and weak tuning of direct optical transition energies and Raman mode frequencies. Electronic structure calculations show the interlayer separation changes with twist due to repulsion between sulfur atoms, resulting in shifts of the indirect optical transition energies. These results show that interlayer alignment is a crucial variable in tailoring the properties of two-dimensional heterostructures.

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Guaranteed-cost consensus for high-order nonlinear multiagent networks with switching topologies is investigated. By constructing a time-varying nonsingular matrix with a specific structure, the whole dynamics of multiagent networks is decomposed into the consensus and disagreement parts with nonlinear terms, which is the key challenge to be dealt with. An explicit expression of the consensus dynamics, which contains the nonlinear term, is given and its initial state is determined. Furthermore, by the structure property of the time-varying nonsingular transformation matrix and the Lipschitz condition, the impacts of the nonlinear term on the disagreement dynamics are linearized, and the gain matrix of the consensus protocol is determined on the basis of the Riccati equation. Moreover, an approach to minimize the guaranteed cost is given in terms of linear matrix inequalities. Finally, the numerical simulation is shown to demonstrate the effectiveness of theoretical results. KEYWORDS guaranteed-cost consensus, Lipschitz nonlinearity, multiagent network, Riccati equation, switching topology INTRODUCTIONConsensus is a typical collection behavior of multiagent networks consisting of a number of autonomous dynamic agents and has been extensively investigated recently due to its wide applications in different fields such as formation and containment control for unmanned aerial vehicles, 1-4 synchronization control for sensor networks, 5,6 and reconfiguration for spacecraft clusters. 7,8 For leadless multiagent networks, the whole dynamics contains 2 parts: the consensus dynamics and the disagreement dynamics, which describe the macroscopical and microcosmic behaviors of multiagent networks, respectively. The consensus dynamics is often described by the consensus function, and the disagreement dynamics is used to determine the consensus and consensualization criteria.According to the dynamics of each agent, multiagent networks can be classified 3 types: first-order ones, second-order ones, and high-order ones. The dynamics of each agent in first-order and second-order multiagent networks is usually described as the first-order and second-order integrators, respectively, whose consensus analysis and design problems can be simplified by these structure features (see other works 9-14 and references therein). Each agent in high-order multiagent networks is often modeled by a general high-order linear system, whose consensus and consensualization criteria are more difficult to be determined since each agent does not have specific structure features compared with first-order Int J Robust Nonlinear Control. 2018;28:2841-2852.wileyonlinelibrary.com/journal/rnc