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A decentralized control scheme can effectively solve the control problem of civil engineering structure vibration under earthquake. This paper takes a research into the decentralized control scheme of adjacent buildings when the earthquake happens. It combines overlapping decentralized control method and linear matrix inequality (LMI) with H ∞ control algorithm and puts forward the overlapping decentralized H ∞ control method. A simplified dynamical model of structural vibration control has been established considering the topology structural features of adjacent buildings. The H ∞ control algorithm is applied into each dynamically different subsystems and can be also served as the decentralized H ∞ controllers. Therefore, by contracting decentralized H ∞ controllers to original state space, overlapping decentralized H ∞ controllers are obtained. In this manner, the adjacent buildings’ structure model is analyzed in terms of simulation and calculation which provides a comprehensive insight into vibration control. The results show that the centralized control, the decentralized control, and the overlapping decentralized control, based on linear matrix inequality, can be nearly effective in cases above satisfactorily. Besides, it can also reduce the computational cost as well as increase the flexibility of controller design.

Taking into account the gravitational potential energy of the piezoelectric energy harvester, the size effect, and the rotary inertia of tip magnet, a more accurate distributed parametric electromechanical coupling equation of tristable cantilever piezoelectric energy harvester is established by using the generalized Hamilton variational principle. The effects of magnet spacing, the mass of tip magnet, the thickness ratio of piezoelectric layer and substrate, and the load resistance and piezoelectric material on the performance of piezoelectric energy capture system are studied by using multiscale method. The results show that the potential well depth can be changed by reasonably adjusting the magnet spacing, so as to improve the energy capture efficiency of the system. Increasing the mass of tip magnet can enhance the output power and frequency bandwidth of the interwell motion. When the thickness of the piezoelectric beam remains unchanged, the optimal load impedance of the system increases along with the increase of thickness ratio of piezoelectric layer and substrate. Compared with the traditional model, which neglects the system gravitational potential energy, the eccentricity, and the rotary inertia of the tip magnet, the calculation results of the frequency bandwidth and the peak power of the modified model have significantly increased.

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