切换规则不确定线性切换系统的鲁棒稳定性

Robust stability of switched linear systems with switching law uncertainty

目前文献中关于线性切换系统稳定性的鲁棒性分析很少 ,论文先利用多项式插值的方法 ,将线性切换系统的一般形式模型转换为矩阵系数多项式模型。然后以矩阵奇异值为分析工具 ,针对线性切换系统的切换规则不确定性 ,讨论了系统渐近稳定的鲁棒性问题。给出了两个系统鲁棒稳定的充分性条件 ,指出后者的保守性比前者更低 。

There are few robustness analyses of switched linear systems. This paper presents a matrix coefficient polynomial description model of switched linear systems using the polynomial interpolation method. Two sufficient conditions for the robust stability of switched linear systems with switching law uncertainty are established based on the matrix singular value method. The conservation requirement of the second condition is much lower than that of the first condition. Finally, a numeric example is given to illustrate the results.