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针对具有输入时滞的结构不确定采样系统,研究了该类系统基于离散化模型的鲁棒控制器设计问题。通过将采样系统的连续的结构不确定对象离散化得到其近似模型,使具有输入时滞不确定采样系统的鲁棒控制器设计问题转换为讨论具有输入时滞的离散系统的鲁棒稳定性问题。利用Lyapunov函数的构造及解析技巧,给出了基于线性矩阵不等式(LMI)的输入时滞离散系统的鲁棒稳定性条件,并在此基础上将控制器参数化,得到了一个通过求解线性矩阵不等式(LMI)来获得采样系统鲁棒控制器的设计方法,所设计的控制器保证了系统的鲁棒稳定性,对结构摄动有着较好的鲁棒性能。最后,通过数值计算仿真验证了本文方法的可行性。
For the uncertain sampling system with input delay, a robust controller design problem based on discretization model is studied. By approximating the discrete model of the sampling system, the robust controller design problem with sampling system with input delay uncertainties is transformed into the robust stability problem of discrete systems with input delay . Based on the construction and analytical technique of Lyapunov function, the robust stability conditions of the input delay discrete-time system based on linear matrix inequality (LMI) are given. Based on this, the controller is parameterized and a solution is obtained by solving the linear matrix Inequality (LMI) to get the design method of robust controller of sampling system. The designed controller guarantees the robust stability of the system and has good robustness to structural perturbation. Finally, the feasibility of this method is verified by numerical simulation.