广义不确定周期时变系统的鲁棒镇定控制

Robust Stabilization Control for Generalized Periodically Time-Varying Uncertain Descriptor Systems

通过广义周期时变系统Lyapunov不等式和广义不确定周期时变系统鲁棒稳定的充分必要条件,讨论了在状态反馈控制下闭环系统的鲁棒镇定问题,得到了系统鲁棒镇定的充分必要条件,且给出了一族状态反馈鲁棒镇定器的设计方法;提出了广义周期时变系统二次稳定的概念,并讨论了二次稳定与鲁棒镇定的关系,得到了广义不确定周期时变系统二次稳定的充分必要条件.最后,通过数值算例说明了主要结果.

Based on the results of Lyapunov inequality and a necessary and sufficient condition of robust stability for generalized periodically time-varying descriptor systems, the robust stability of a closed-loop system under state feedback control is discussed with its necessary and sufficient condition given, and then the design method for a class of state feedback robust controllers is presented. Introducing the definition of quadratic stability and analyzing the relation between quadratic stability and robust stability of the systems, the necessary and sufficient condition of quadratic stability is obtained for generalized periodically timevarying uncertain descriptor systems. A numerical example is given to prove the conclusion drawn from the discussion.