二维线性连续系统稳定性的新判据

New stability criterion for 2D linear continuous systems

提出了一个检验二维线性连续系统稳定性的新算法。该算法基于多项式判别系统理论,可以对系统稳定与否作出完备的判断,克服了传统频域方法需要取大量频率点进行检验且只能提供近似结论的不足。更重要的是,此算法可以用于分析含参数系统的稳定裕度。实际案例显示了该算法的有效性。

In this paper, a new stability criterion is proposed for testing 2D linear continuous sys- tems. This algorithm is based on the discriminant systems of real polynomials, and can give a complete answer for whether a 2D system is stable or not, thus overcoming the limitations of traditional methods that a large mount of frequency points should be tested and only inaccurate results can be provided. More importantly, it can be used to analyze the stability regions of 2D systems with parameters as well. Examples show the validity of our algorithm.