Zhang Xuefeng, Wang Zhe
School of Sciences, Northeastern University, Shenyang, Liaoning, 110819, China.
School of Sciences, Northeastern University, Shenyang, Liaoning, 110819, China.
ISA Trans. 2020 Aug;103:1-9. doi: 10.1016/j.isatra.2020.03.019. Epub 2020 Mar 18.
In this paper, the stability and robust stabilization of switched fractional order systems are concerned. Firstly, two stability theorems for switched fractional order systems with order 0<α<1 and 1<α<2 under the arbitrary switching law are given. Secondly, the relationship between the stability of switched integer order systems and that of switched fractional order systems is obtained. Finally, the robust stabilization of uncertain switched fractional order systems under the common switching law is further discussed. The state feedback control gains are obtained under both the sensor and actuator faults in terms of linear matrix inequalities. A practical electrical circuit example and four numerical simulation examples are presented to show the effectiveness of our results.
本文研究了切换分数阶系统的稳定性和鲁棒镇定问题。首先，给出了0<α<1和1<α<2阶切换分数阶系统在任意切换律下的两个稳定性定理。其次，得到了切换整数阶系统的稳定性与切换分数阶系统的稳定性之间的关系。最后，进一步讨论了不确定切换分数阶系统在常见切换律下的鲁棒镇定问题。利用线性矩阵不等式，在传感器和执行器故障情况下均获得了状态反馈控制增益。给出了一个实际电路实例和四个数值仿真实例，以验证本文结果的有效性。
