广义系统渐近稳定分析与镇定的Lyapunov方法

Asymptotic stability analysis and stabilization for generalized systems via Lyapunov methods

利用Lyapunov方法研究了广义系统的渐近稳定性分析及控制问题,首先提出一种新形式的Lyapunov方程,用来研究广义系统渐近稳定性与镇定问题,同时给出了利用Lyapunov方程判定具有脉冲形式下广义系统渐近稳定的充分必要条件。利用相应的Riccati方程完成镇定广义系统的状态反馈控制器的设计。本文所有结论对广义系统有无脉冲行为均适用。最后利用数值例子说明主要结果。

We investigate the problems of stability and stabilization for linear time-invariant generalized systems using Lyapunov methods. First, a new type of Lyapunov equation is presented to solve the asymptotic stability of generalized systems, necessary and sufficient conditions for the impulses generalized systems to be asymptotically stable are derived. Then state feedback law is designed using corresponding Riccati equation to stabilize the systems. All results are valid for impulse and non-impulse generalized systems. Finally, numerical examples are given to illustrate the results.