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针对一类同时具有变时滞和连续分布时滞的分布参数系统的状态反馈控制问题进行了研究,通过选择适当的Lyapunov-Krasovskii函数,采用线性矩阵不等式(LMI)方法,得到了变时滞闭环系统渐近稳定的一个充分条件.设计了无记忆的状态反馈控制器,使得在一个正定矩阵存在的条件下,闭环系统是可镇定的,从而得到了常时滞分布参数系统可镇定的一个推论.最后,通过一个数值仿真例子说明了所给出设计方法的可行性和有效性.
A class of state feedback control problems for distributed parameter systems with both variable delays and continuous distributed delays are investigated. By choosing the appropriate Lyapunov-Krasovskii function and using the linear matrix inequality (LMI) method, A sufficient condition for the asymptotic stability of the system is established. The memoryless state feedback controller is designed so that the closed-loop system is calibratable in the presence of a positive definite matrix, so that a corollary of the system with constant delay distributed parameters is obtained. Finally, a numerical simulation example is given to illustrate the feasibility and effectiveness of the proposed design method.