不确定奇异分数阶系统的正则和鲁棒稳定

摘要

The robust stability and stabilization of uncertain descriptor fractional‐order systems are investigated .In such systems parameter uncertainty is assumed to be time‐invariant and norm‐bounded in the state matrix .First ,a predictive controller was used to regularize the uncertain descriptor fractional‐order systems , and then an output feedback controller was designed to stabilize the regularized system .The sufficient conditions for robustly stabilizing such systems with the fractional order alpha in [1 ,2) are derived .Finally ,a numerical example is provided to demonstrate the effectiveness of the proposed approach .%研究了不确定奇异分数阶系统的鲁棒稳定和镇定问题。在该系统里，状态矩阵的不确定参数通常假定为时不变和范数有界的。首先设计一个可预测的控制器使得不确定奇异分数阶正则；然后设计一个输出反馈控制器使得正则后的系统稳定，这样可以得到当分数阶阶次在[1，2）时系统鲁棒渐近稳定的充分条件；最后通过一个数值仿真证明了该方法的有效性。