Lurie系统的鲁棒量化控制

Robust quantized control for Lurie systems

研究了Lurie系统的鲁棒量化状态反馈控制问题,其中的量化器为静态对数量化器.首先,根据Lurie系统自身特点以及对数量化器的特性,将量化状态反馈控制作用下的Lurie系统建模成具有两个扇形约束的不确定系统.然后分别考虑了没有量化和有量化作用两种情形,利用小增益定理,得到了闭环系统内稳定的充分必要条件,并进一步给出了相应的状态反馈控制律.最后,数值例子表明了本文方法的有效性.

The robust quantized state-feedback control for Lurie systems is addressed, where the static logarithmic quantizer is considered. According to the characteristics of the Lurie systems and the properties of the logarithmic quantizer, the Lurie systems with quantized statefeedback control are modeled as uncertain systems with two sector constraints. Then, by applying the small gain theorem, we establish a sufficient and necessary condition of internal stability for the closedloop system with or without quantization effect, respectively. The corresponding state feedback control law is also developed. A numerical example is given to illustrate the effectiveness of the method proposed.