不确定时滞系统基于观测器的鲁棒非脆弱控制

Robust non-fragile observer-based control of time-delay systems with uncertain parameters

为了同时考虑系统参数不确定性和控制器不确定性对系统性能的影响,提出了不确定时滞系统基于观测器的鲁棒非脆弱控制器设计方法.基于Lyapunov-Krasovskii理论,得到系统鲁棒非脆弱控制器存在的充分条件.当控制矩阵为列满秩时,采用矩阵奇异值分解(SVD)的方法,将控制器的存在条件转化为一个严格线性矩阵不等式(LMI)的可解性问题,易于用Matlab/LMI工具箱进行求解.数值算例表明,所设计的控制器对系统参数的不确定性、控制器和观测器的不确定性都具有较好的鲁棒性.

The design method of a robust non-fragile observer-based controller for uncertain time-delay systerns was presented to consider the effects on system performances arising from the uncertainties of both parameters and controllers. A sufficient existence condition of the controller was obtained based on Lyapunov-Krasovskii theory. If the control matrix is full column rank, the existence condition is formulated in terms of a linear matrix inequality （LMI） by singular value decomposition （SVD） technique, which can be solved efficiently by employing Matlab/LMI Toolbox. Numerical examples show that the designed controller is robust to the system parametric uncertainties and the controller＇s and observer＇s uncertainties.