主要考虑了基于观测器的Lurie网络化控制系统的绝对稳定性问题. 由于采用了基于观测器的反馈控制器, 传感器到控制器的网络诱导时延和控制器到执行器的网络诱导时延不再能合并到一起处理. 首先通过状态增广方法将Lurie网络化控制系统建模为一个多时滞的Lurie系统, 然后利用Newton-Leibniz公式和添加自由权矩阵的方法给出了时滞依赖的稳定性条件. 在此基础上, 给出三种求解控制器和观测器增益矩阵的方法. 此外, 还分别给出了被控对象存在范数有界不确定性和结构不确定性时系统的鲁棒稳定性条件及鲁棒控制器设计方法, 所有得到的结果都是以线性矩阵不等式的形式给出的. 便于利用线性矩阵不等式工具包进行求解. 最后, 通过两个仿真算例说明了方法的可行性和有效性.
This paper is concerned with the absolute stability problem for observer-based Lurie networked control systems. Due to utilizing observer-based dynamic feedback controller, the network-induced delays can not be simply thought as the sum of the sensor-to-controller delay and the controller-to-actuator delay. First, the Lurie networked control system is modeled as a multiple delay Lurie system by the state augment approach. Then, a delay-dependent stability condition is established via Newton-Leibniz formulation and free weighting matrices. Based on the obtained result, three approaches to calculate the controller gain matrix and the observer gain matrix are proposed. We also present the robust stability condition and robust controller design approach for Lurie networked control systems with norm-bounded uncertainties and structured uncertainties. All the results are formulated in terms of linear matrix inequalities (LMIs), which are easily solved via the LMI toolbox in Matlab. Finally, two examples are worked out to illustrate the feasibility and effectiveness of the proposed approaches.