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The attachment process and response to an antitumor reagent for cultured cells were monitored with a quartz crystal microbalance (QCM) combined with a microscope. To fit the experimentally obtained curves of the resonant frequency, model equations of resonant frequency curves were built, and parameters of time constants and scale coefficients were determined. For the cell attachment process, a first-order lag response curve well fit the experimental curves. For the response to cisplatin, two response steps were observed in both QCM data and microscopic images, where the cells loosened in the first step and shrank in the second step. Resonant frequency responses for both processes were well fit by two logarithmic normal distribution functions. In addition, the dependence of the resonant frequency change on the cell number was also studied, and a cell–cell interaction model for attached cells was proposed to explain the saturation of the resonant frequency change in high density cell seeding.

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Solving bilinear matrix inequality (BMI) problems appearing in robust control by deterministic strategy is quite hard. We propose a branch and bound method for BMI optimization problems where a randomized algorithm is used in the bounding procedure. Computational experiments demonstrate the effectiveness of the proposed method.

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