This brief discusses the stability and stabilization of a class of fractional-order nonlinear systems with Caputo derivative. On the basis of the stability theory of fractional-order linear differential equation, Mittag-Leffler function, Laplace transform, and the Gronwall inequality, two sufficient conditions are derived for the asymptotical stability of a class of fractional-order nonlinear systems with fractional-order α : 0 < α ≤ 1 and 1 < α < 2, respectively. Then, two sufficient conditions for asymptotical stabilization of such fractional-order systems are obtained, in which feedback gains could be ensured by the pole placement technique. Finally, some numerical examples are provided to show the validity and feasibility of the proposed method.
A microfabricated high-throughput cell electrofusion chip with 1,368 pairs of high aspect ratio silicon microelectrodes is presented. These microelectrodes, which were distributed in six individual microscale cell-fusion chambers, were covered with titanium and gold thin film to improve their electric conductivity as well as surface hydrophobility. Six chambers having different electrode distances make the chip highly suitable for fusing cells with different sizes. A microfluidic platform was set up for flowing control, cell manipulation and also experimental observation. Cells for electrofusion were first aligned at the prearranged locations by the dielectrophoretic force between two counter-electrodes, which benefits the traverse of electric pulse through the cell-cell contacting point for electroporation. Several on-chip cell electrofusion experiments have been carried out on different kinds of animal cells and plant protoplasts. Compared with conventional electrofusion methods, higher fusion efficiency was achieved on this device for precisely forming micropores on the proximate membranes of two contacting cells, and high throughput was also obtained due to the use of a large number of microelectrodes for cell manipulation and fusion. Moreover, a much lower power supply was required for the shorter distance between two counter-electrodes.
Based on cylindrical algebraic decomposition (CAD) technique, an algorithm for solving the stable parameter region of factional-order systems with structured perturbations (FOSSP) is presented. The algorithm is nonconservative and universal for fractional order systems with order 0 < α < 2. And the computational complexity of the algorithm is less than existing methods. Two examples are given to show the effectiveness of the proposed method.
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