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针对一类含有分布时滞的线性退化系统,研究其稳定性以及反馈控制器的设计问题.首先基于闭环系统的中立型模型变换,然后利用descriptor form方法,再通过依赖于时滞参数的Lyapunov-Krasovskii泛函的设计,得到了此类系统渐近稳定的充分条件,并以线性矩阵不等式(LMI)的形式给出了结果,随之将控制器的设计问题转化成了LMI求可行解问题,使得控制器参数易于求解,最后通过数值例子验证了结论的有效性和可行性.
For a class of linear degenerate systems with distributed delays, the stability of the system and the design of the feedback controller are studied. First, a neutral model transformation based on a closed-loop system is used. Then, descriptor form method is adopted, and then the Lyapunov- The sufficient conditions for the asymptotic stability of such a system are obtained by the design of the Krasovskii functional, and the results are given in the form of linear matrix inequalities (LMIs). Then the design problem of the controller is converted into a feasible solution of LMI. The parameters of the controller are easy to solve. Finally, the numerical example is used to verify the validity and feasibility of the conclusion.