人工胰岛素泵生理系统全局指数渐近稳定性与血糖稳定

摘要

研究了人工胰岛素泵实现血糖水平稳定性问题.首先证明了该生理系统解的正有界性.由于构造合适的Lyapunov泛函比较困难,采用了新的方法,把该非线性时滞系统转化为系数时变线性时滞系统,构造Lyapunov泛函并利用Razumikhin定理得到了其唯一平衡点的全局指数渐近稳定性条件.结果表明,当技术时滞τ1充分小时,全局指数渐近稳定,血糖水平稳定,易于达到疗效.%The stability problem of glucose level was considered by artificial pancreas. At first, the posi-tivity and boundness of this physiological system were proven. Due to the difficulty of the appropriate Lya-punov functional construction, the new approach was employed. The nonlinear DDEs were transformed into the linear DDEs with the time-dependent coefficients. Then the Lyapunov functional was constructed and the global exponential asymptotic stability conditions of the unique equilibrium were obtained by the Razumikhin Theorem. The result showed that if the technolgical delay T1 was sufficiently small, the global exponential asymptotic stability and the glucose stability were obtained. Its clinical efficiency could be easily obtained.