时滞Lipschitz离散时间广义系统解的存在性与稳定性

Existence and Stability of Solution of Lipschtiz Discrete-Time Descriptor Systems with Time-Delay

讨论了带有时滞的Lipschitz离散时间广义系统(LDDD)的解的存在唯一性与稳定性问题.利用不动点原理,给出保证LDDD系统解存在唯一的矩阵不等式准则;利用线性矩阵不等式,给出LDDD系统解存在唯一的条件;证明由该线性矩阵不等式可以同时得到LDDD系统的全局指数渐进稳定性,即给出了LDDD系统全局指数渐进稳定的一个充分条件.另外,还证明了解的存在唯一性不等式准则与对系统的分解矩阵的选取是无关的.最后,给出具体的实例说明这种方法的可行性.

This paper discusses the existence and uniqueness of solution and its stability for Lipschtiz discrete-time descriptor systems with time-delay （LDDD）. Firstly, by means of fixed point principle, a matrix inequality criterion which guarantes the existence and uniqueness of solution is presented. Then secondly, the existence and uniqueness of solution are also proved via linear matrix inequality. Thirdly, a sufficient condition is presented via this linear matrix inequality under which the solution is globally exponentially stable. In addition, it is easy to verify that the criterion presented is independent of the choices of decomposition matrices for the given system. Finally, the approach is illustrated by a numerical example.