一般广义周期时变系统的允许性分析

Analysis of admissibility for general periodically time-varying descriptor systems

研究了一般广义周期时变系统的允许性问题.通过对正常周期时变系统和广义周期时变系统Lyapunov不等式的深入分析,建立了一般广义周期时变系统的Lyapunov不等式,把一般广义周期时变系统的允许性问题转化为Lyapunov不等式的数值解问题.首先,得到了一般广义周期时变系统的第一受限等价系统允许的充分必要条件;而后,又利用等价变换得到了一般广义周期时变系统允许的充分必要条件.最后,通过数值算例说明了本文的主要结果.

The admissibility problem for general periodically time-varying descriptor systems was discussed. By unalyzing Lyapunov inequalities of normal periodically time-varying systems and periodically time-varying descriptor systems, Lyapunov inequalities of general periodically time-varying descriptor systems were established, and the admissibility problem was deduced into the numerical solution for the Lyapunov inequalities. Firstly, a sufficient and necessary condition admissible for first restrained equal systems of general periodically time-varying descriptor systems is obtained. Then a sufficient and necesary condition admissible for general periodically time-varying descriptor systems is derived by equal changing. The present results get proved by the digital examples.