变周期采样控制系统的稳定性分析

Stability analysis of variable period sampling control system

运用类Lyapunov泛函研究变周期采样控制系统的稳定性问题。在构造类Lyapunov泛函过程中,增加泛函中某一项矩阵的维数,充分利用系统的采样信息;在估计类Lyapunov泛函导数过程中,充分运用现有的相关积分不等式进行放缩;最后,使用线性矩阵不等式技术推出保守性较小的系统稳定性准则。数值算例表明,提出的系统稳定性定理具有较小的保守性,验证了方法的有效性和优越性。

The stability of variable period sampling control systems is studied by using Lyapunov-like functional.In the process of constructing Lyapunov-like functional,the dimension of a matrix in the functional is increased to make full use of the sampling information of the system.In the process of estimating Lyapunov-like functional derivatives,the existing relevant integral inequalities are fully used for scaling and shrinking.Finally,a less conservative system stability criterion is derived by using linear matrix inequality technique.Numerical examples show that the proposed system stability theorem is less conservative,the effectiveness and the superiority of the method are verified.